The Elon Musk-led Department of Government Efficiency is dealing with some growing pains.

The newly minted department has lost a co-chair and legal counsel and faces several lawsuits. Some Trump loyalists are questioning Mr. Musk’s focus, while others wonder if he is too enthralled with the political limelight or only trying to advance his business empire.

It is an inauspicious start for a group that President Trump initially described as “the Manhattan Project of our time” with a mission to “dismantle Government Bureaucracy, slash excess regulations, cut wasteful expenditures, and restructure Federal Agencies.”

For his part, Mr. Musk is casting things in a positive, forward-looking light. Mr. Musk, who is also the world’s richest man, recently highlighted DOGE’s claim that it has already saved the federal government $1 billion a day by “stopping the hiring of people into unnecessary positions,” halting diversity, equity, and inclusion programs, and stopping improper payments to foreign organizations.

“Progress,” Mr. Musk posted on X.

The White House did not respond to a request for comment about the early challenges facing DOGE.

But White House press secretary Karoline Leavitt sang the group’s praises, telling reporters at a daily briefing that  DOGE and the Office of Management and Budget stopped $37 million from going “out the door” to the World Health Organization, which Mr. Trump had pulled the U.S. out of.

“DOGE and OMB also found that there was about to be $50 million taxpayer dollars that went out the door to fund condoms in Gaza,” she said. “That is a preposterous waste of taxpayer money.”

Those two moves alone saved taxpayers $87 million.

Still, Mr. Musk and DOGE have a bullseye on their back.

Longtime Trump ally Stephen K. Bannon and others have raised concerns that Mr. Musk must focus more on the massive task and stop trying to get involved in other things the administration is doing.

Conservative commentator Erick Erickson said Mr. Musk “needs an intervention because I think he is becoming Icarus,” the mythical Greek craftsman who made himself a set of wings but flew too close to the sun and died.

Mr. Musk is also on shaking footing with voters, according to a Quinnipiac University poll this week that found voters disapprove of him having a prominent role in the Trump administration by 53% to 39%.

Meanwhile, biotech millionaire and failed presidential candidate Vivek Ramaswamy, whom Mr. Trump tapped to co-chair DOGE, stepped down after reportedly clashing with Mr. Musk over the commission’s path forward. 

“It was really just an actual mutual decision,” Mr. Ramswamy said on the “Breakfast Club” radio show.

Charlamagne tha God, a co-host of the program, did not buy Mr. Ramaswamy’s explanation.

“I think you got pushed out, or you know that it is going to implode,” he said. “I think you know Elon is going to crash and burn.”

Then, the news broke that legal counsel William McGinley was leaving DOGE to pursue a job in the private sector.

The board also faces lawsuits, including one that says it violated federal law regulating the transparency and makeup of federal advisory committees.

The Trump administration faced similar pushback after he launched the Presidential Advisory Commission on Election Integrity in 2017.

Hans von Spakovsy, a senior legal fellow at the Heritage Foundation who served on the voter fraud commission, said he sees “great similarity” between the two situations. 

In addition to lacking executive authority to implement their final recommendations, Mr. von Spakovsy said both groups faced “blowback from the institutional left, their friends in the media, and even parts of the federal ‘swamp,’ was immediate and totally out of control.”

“They were threatened by the very idea that [the voter fraud commission] would even study the problems and identify possible solutions,” he said. “DOGE is in the same position except that it represents an even bigger threat.”

Brian Riedl, senior fellow at the Manhattan Institute, a conservative think tank, said he believes DOGE can play an essential role on the spending front if it dials down its expectations.

“My recommendation was that DOGE focus narrowly on inefficiency and government waste, making programs operate more efficiently, rather than going on ideological quests to get rid of programs that a couple of GOP billionaires don’t like because Congress would never approve that anyway,” Mr. Riedl said.

He said that involves steering clear of efforts to eviscerate federal agencies.

“If Congress was going to eliminate the Department of Education, they would have eliminated the Department of Education already,” he said. “They don’t need Elon Musk to write it in a report. And that’s why, I think, it’s kind of a waste of time for them to do stuff like that.”