President Trump and Elon Musk promised taxpayers big savings, maybe even a “DOGE dividend” check in their mailboxes, when the Department of Government Efficiency was let loose on the federal government. Now, as he prepares to step back from his presidential assignment to cut bureaucratic fat, Mr. Musk has said without providing details that DOGE is likely to save taxpayers only $150 billion.

That is about 15 percent of the $1 trillion he pledged to save, less than 8 percent of the $2 trillion in savings he had originally promised and a fraction of the nearly $7 trillion the federal government spent in the 2024 fiscal year.

The errors and obfuscations underlying DOGE’s claims of savings are well documented. Less known are the costs Mr. Musk incurred by taking what Mr. Trump called a “hatchet” to government and the resulting firings, agency lockouts and building seizures that mostly wound up in court.

The Partnership for Public Service, a nonprofit organization that studies the federal work force, has used budget figures to produce a rough estimate that firings, re-hirings, lost productivity and paid leave of thousands of workers will cost upward of $135 billion this fiscal year. At the Internal Revenue Service, a DOGE-driven exodus of 22,000 employees would cost about $8.5 billion in revenue in 2026 alone, according to figures from the Budget Lab at Yale University. The total number of departures is expected to be as many as 32,000.

Neither of these estimates includes the cost to taxpayers of defending DOGE’s moves in court. Of about 200 lawsuits and appeals related to Mr. Trump’s agenda, at least 30 implicate the department.

“Not only is Musk vastly overinflating the money he has saved, he is not accounting for the exponentially larger waste that he is creating,” said Max Stier, the chief executive of the Partnership for Public Service. “He’s inflicted these costs on the American people, who will pay them for many years to come.”

Mr. Stier and other experts on the federal work force said it did not have to be this way. Federal law and previous government shutdowns offered Mr. Musk a legal playbook for reducing the federal work force, a goal that most Americans support. But Mr. Musk chose similar lightning-speed, blunt-force methods he used to drastically cut Twitter’s work force after he acquired the company in 2022.

“The law is clear,” said Jeri Buchholz, who over three decades in public service handled hiring and firing at seven federal agencies, including NASA and the Defense Intelligence Agency. “They can do all the things they are currently doing, but they can’t do them the way they’re doing them. They can either start over and do it right, or they can be in court for forever.”

Harrison W. Fields, a White House spokesman, defended DOGE’s cuts and called the $150 billion that the administration had saved “monumental and historic.”

“It’s important to realize that doing nothing has a cost, too, and these so-called experts and groups are conveniently absent when looking at the costs of doing nothing,” he said.

On the I.R.S., he said, “Every single cut has been done to make the government more efficient and not to be a burden to the American people or cut any critical resources or programs they rely on.”

Based on the latest available information, the DOGE cuts have targeted at least 12 percent of the 2.4 million civilian employees in the federal work force. But a wide gap exists between DOGE’s planned cuts and the number of people who actually leave.

Buyouts and firings initially trimmed about 100,000 workers — thousands fewer people than those who typically retire in a year, according to Office of Personnel Management figures. At least one-quarter of those 100,000 workers have been rehired at full pay, most after judges ruled that their firings were illegal and some after Mr. Musk said DOGE had “accidentally” sacked workers safeguarding nuclear weapons, ensuring aviation safety and combating bird flu and Ebola.

When judges ordered that the workers be hired back, the government put them on paid leave, meaning taxpayers would foot the cost of rehiring them, plus the salaries they collected while staying home.

Layoffs of 10,000 employees at the Department of Health and Human Services wiped out the entire team at the Centers for Disease Control and Prevention combating H.I.V. around the world. In an interview, two public health physicians said they were caught off guard because the team’s work always had bipartisan support. They were facing termination on June 2 and said they wanted to return to work but did not know to whom to make their case.

Mr. Musk’s methods have cast a pall over the latest effort by an American president to trim the federal bureaucracy, as most Americans say they want. In congressional town halls and interviews, even Trump voters have said they are tired of Mr. Musk’s bloodletting. In a poll released this month, 58 percent of those surveyed said they disapproved of how Mr. Musk was handling DOGE’s work, and 60 percent disapproved of Mr. Musk himself.

‘We Will Make Mistakes’

A week after Mr. Trump’s inauguration, the Office of Personnel Management sent a now infamous email to more than two million federal workers with the subject line “Fork in the Road.” They were told they could either resign and be paid through September or risk being sacked down the road.

The email ignited anger and confusion over whether DOGE had the legal authority to pay workers through September. Federal employee unions sued, but a judge allowed the program to go forward. About 75,000 people left, or about three percent. If the administration does not renege on its offer, it will be paying their salaries into the fall.

The mass buyout did not favor highly rated performers nor distinguish crucial jobs from nonessential ones, practices that guided furloughs during past government shutdowns. Consequently, the administration wound up trying to reverse an exodus of people in vital roles.

“We will make mistakes,” Mr. Musk told cabinet members in February. After he boasted of feeding the United States Agency for International Development “into the wood chipper,” a move a judge later found violated the Constitution, Mr. Musk discovered that “one of the things we accidentally canceled very briefly was Ebola prevention.” But his claim to have swiftly repaired the damage was inaccurate.

Separately, a New York Times investigation into cuts to the National Nuclear Security Administration illustrate the effect of the buyouts on efforts to safeguard and modernize the nation’s nuclear weapons. Of more than 130 people who were fired or accepted DOGE’s invitation to quit, at least 27 were engineers, 13 were program or project analysts, 12 were program or project managers, and five were physicists or scientists.

Four of these employees were specialists handling the secure transport of nuclear materials, and a half dozen worked in the agency unit that builds reactors for nuclear submarines.

“Those are such hard jobs to fill, because people could make as much or more money working for the plant or laboratory itself,” said Jill Hruby, who led the National Nuclear Security Administration during the Biden administration.

Several people on the nuclear safety team found new jobs with the government contractors they once supervised. Across government, a disproportionate number of professionals in high demand by the private sector have quit, according to Mr. Stier.

“There are plenty of people who are best in class who are sticking it out because they’re so purpose-driven,” he said. “But it’s easier for someone who has options to say, ‘This is crazy, I’m not going to do this anymore,’ and go someplace else.”

‘Money Being Deliberately Wasted’

In mid-February, the Office of Personnel Management targeted all 220,000 of the federal government’s probationary employees, who are new or newly promoted professionals serving a one- to two-year trial period with fewer worker protections. They included a cadre of younger, tech-savvy professionals hired at great expense to replace a wave of baby boomer retirees. Hiring and training them cost about $10,000 for a clerical worker to more than $1 million for an elite spy.

“This is the equivalent of a major-league baseball franchise firing all of their minor-league players,” said Kevin Carroll, a former C.I.A. officer and lawyer who represents some of the fired workers. “It’s a huge amount of money being deliberately wasted.”

About 24,000 probationary employees across nearly 20 agencies had been fired by March 13, when a federal judge in Maryland ruled that the cuts were illegal and ordered the agencies to rehire the workers, but the government appealed and the legal wrangling continues. By law, probationary employees can only be fired for cause, typically for poor performance, Judge James K. Bredar of the Federal District Court in Maryland said in a lengthy ruling.

He ordered the government to recall the fired workers, including 7,600 from the Treasury Department, 5,700 at the Agriculture Department and more than 3,200 at the Department of Health and Human Services, according to court filings. But the administration instead put them on paid leave, where they collect annual salaries averaging $106,000 while waiting in limbo.

For each probationary worker DOGE idled, the government lost thousands of dollars it spent on recruitment, hiring incentives, security clearances and training, an investment normally recouped over years of service. In one case, a fired probationary employee with the Department of Health and Human Services received a pay raise after she was reinstated and put on paid leave.

The administration cut about 400 probationary workers at the Federal Aviation Administration after multiple plane crashes, including one in Washington in January that killed 67 people. The layoffs included maintenance mechanics and aviation safety assistants.

The C.I.A. confirmed last month that some officers hired in the past two years had been summoned to a location away from the agency’s headquarters in Langley, Va., and asked to surrender their credentials to security personnel. About 80 officers were let go.

Senator Mark Warner of Virginia, the ranking Democrat on the Intelligence Committee, said it cost $400,000 to get a C.I.A. recruit through the security clearance process and specialized training.

Inflicting Pain

The theatrics around the firings, including an appearance by Mr. Musk at a conservative political convention waving a chain saw, suggest they are also about inflicting pain on a bureaucracy Mr. Trump perceives as a subversive “deep state.”

That was a goal for federal employees set by Russell T. Vought, who now leads the Office of Management and Budget. “When they wake up in the morning, we want them to not want to go to work, because they are increasingly viewed as the villains,” Mr. Vought told a conservative gathering in 2023.

Ms. Buchholz and Mr. Stier emphasize that the government is indeed inefficient and needs reform. But by “gleefully torturing people,” Ms. Buchholz said, DOGE has hurt the government’s ability to recruit young, talented workers to lead a modernization.

“This country historically has had an independent public service that attracts people focused on service to Americans,” Ms. Buchholz said. “But this administration values the kind of service you get from political appointees, who serve at the president’s pleasure.”

Reporting was contributed by Eileen Sullivan, Andrew Duehren, Sharon LaFraniere, Minho Kim, Julie Tate, Zach Montague and Adam Goldman from Washington. Kitty Bennett contributed research.

Stocks rose on Thursday, extending a two-day rally as investors hope for an easing of President Trump’s trade wars and weigh comments on its impact from a Federal Reserve official.

The S&P 500 gained more than 1 percent after stalling in early trading. The index has seesawed this week: Monday saw a sharp sell-off, followed by two days of sizable gains after Mr. Trump on Tuesday said that he was prepared to be “very nice” in trade negotiations with China.

The rally then paused after officials in China said they were not holding talks with the United States about easing trade tensions. But indexes continued to swing on scraps of information about tariffs and monetary policy, in the absence of concrete developments about the escalating global trade war.

On Thursday, Christopher Waller, a Fed governor, told Bloomberg that the economic hit from Mr. Trump’s tariffs will take time to show up in the data, suggesting that the central bank is not poised to lower interest rates soon. But when asked what would prompt him to favor a rate cut, Mr. Waller said, “If I saw enough movement in the unemployment rate to make me think that things were going bad, or growth prospects started tanking, or consumer spending started really going down, then I’d be ready to go.”

He Yadong, a spokesman for China’s Ministry of Commerce, said on Thursday that, “There are currently no economic and trade negotiations between China and the United States, and any claims about progress in China-U.S. economic and trade negotiations are baseless rumors without factual evidence.”

A spokesman for China’s Ministry of Foreign Affairs, Guo Jiakun, reiterated China’s stance, which is that the tariff war was started by the United States and that China would only engage in talks under certain conditions. “China’s attitude is consistent and clear: If you want to fight, we will fight to the end; if you want to talk, the door is open,” he said.

The day before, Treasury Secretary Scott Bessent dismissed speculation that Mr. Trump was considering unilaterally lowering tariffs on China and emphasized that any moves to de-escalate trade tensions would need to be mutual. “I don’t think either side believes that the current tariff levels are sustainable,” he said.

In other developments on Thursday:

• Big companies reporting their latest earnings warned that tariffs and economic uncertainty would dent profits in the months ahead. PepsiCo and Merck cut their earnings forecasts, while American Airlines withdrew its previous forecast for the rest of the year, until “the economic outlook becomes clearer.”

• A rise in major technology stocks boosted the tech-heavy Nasdaq Composite index, which was roughly 2 percent higher. Shares in Amazon were up more than 2 percent, as were shares in the chip giant Nvidia.

• The U.S. dollar fell against several major currencies, including the euro, the British pound and the Japanese yen.

• The yield on 10-year Treasury bonds, which move inversely to prices, fell to 4.32 percent.

• Oil futures recovered some ground, with Brent crude up nearly 1 percent, approaching $67 a barrel.

• Stocks in Asia and Europe were mixed: Japan’s main index was up, Hong Kong and South Korea were down, and markets in Britain, France and Germany were roughly flat.

Colby Smith and Danielle Kaye contributed reporting and Siyi Zhao contributed research.

Officials in the United States are urging Japan and South Korea to make a formal commitment within the next few weeks to a $44 billion natural gas project in Alaska.

The effort, known as Alaska L.N.G., is a centerpiece of President Trump’s energy agenda, and aims to ship gas from northern Alaska in a liquefied form to nations in Asia. Its feasibility hinges on securing backing from the region, home to some of the world’s largest purchasers of liquefied natural gas.

A group advising Mr. Trump on domestic energy production, the National Energy Dominance Council, is seeking to convene officials from the trade ministries of both Japan and South Korea for a summit in Alaska on June 2, according to three people with knowledge of the confidential outreach who requested anonymity.

The project’s proponents want to be able to announce at the summit that they have received signed letters of intent from Japan and South Korea to invest in Alaska L.N.G. or purchase its gas, the people said. Taiwan formally signed a similar letter of intent to purchase gas from Alaska L.N.G. last month.

The White House, as well as the Japanese and South Korean trade ministries, did not respond to requests for comment.

Alaska L.N.G., first proposed more than a decade ago, had been considered by many in the energy industry to be a long shot. But it occupies a prominent spot in Mr. Trump’s efforts to reshape the U.S. energy landscape and restore momentum for fossil fuels.

The plan is to construct an 800-mile pipeline from fields north of the Arctic Circle to southern Alaska. From there, the gas would be cooled into liquid form and shipped on tankers to Asia.

For Asian countries, shipping L.N.G. from Alaska would be cheaper and quicker than importing it from many of their traditional sources, including Australia, the Middle East and the Gulf Coast of the United States.

But major Asian buyers of the fuel, including Japan, have long been cautious about the Alaska L.N.G. project because of its substantial costs, and doubts that it would actually be able to get off the ground.

On his first day in office, Mr. Trump signed an executive order aimed at “unleashing” Alaska’s energy potential, including the pipeline proposal.

Japan, South Korea and Taiwan face the possibility of additional double-digit-percentage tariffs, which have been imposed by Mr. Trump on numerous U.S. trading partners. Economists have warned that the tariffs, which have been paused until early July, could severely slow economic growth if they take effect.

Japan, which initiated tariff talks with the United States last week, has indicated that pledges to purchase more American liquefied natural gas would be a significant component of its offer to the administration. South Korea has made similar promises and is set to begin negotiations in Washington on Thursday.

Last month, Taiwan’s state oil and gas company, CPC, signed a letter of intent to buy six million metric tons of gas from Alaska L.N.G. That would represent almost a third of the total amount of liquefied natural gas Taiwan imported last year.

Mr. Trump has said he believes that countries in Asia would sign on to support the Alaska project. During his address to Congress in March, he said Japan and South Korea wanted to invest “trillions of dollars each” in the project, a statement that took officials in Tokyo and Seoul by surprise. He did not clarify how the project, which isn’t expected to begin shipping liquefied gas until the early 2030s, would receive trillions in investment.

In Japan, and most likely elsewhere, the challenge will be securing private-sector buyers willing to align with government plans and enter into long-term agreements to purchase gas from Alaska L.N.G. In Japan, U.S. officials see three energy companies — Jera, Tokyo Gas and Inpex — as potential customers, two of the people familiar with the matter said.

Many remain wary of the economics of such a deal. Letters of intent to participate in the project are likely to include room to withdraw. Alaska L.N.G. says the price of its gas would be competitive when it begins operations.

Kiuko Notoya and Jin Yu Young contributed reporting