Has Elon Musk become too big to tame?

For Elon Musk, the word refers to taming a federal bureaucracy that has run amok.

For others, it is about Musk himself: Has the world’s richest man, adviser to President Trump, leader of six companies from Tesla to SpaceX, become too big to be held accountable?

The question arises as he stands in the West Wing victoriously beside the president, after having written big checks to support Republicans, successfully fought their political battles and amplified their messages on his social-media platform, X.

The debate takes on greater urgency after he joined Vice President JD Vance in questioning the legitimacy of the courts’ power to rule on actions taken by Musk’s government efficiency efforts at DOGE. And as Musk challenges the integrity of Democratic members of Congress voicing concerns he is overstepping.

“All aspects of the government must be fully transparent and accountable to the people," Musk posted on X this past week, one of many tweets about the government, including many that dealt with rooting out supposed “fraud."

Since Trump entered office last month and Musk’s role leading DOGE took center stage, the president has been asked often about what steps are being taken to ensure there aren’t conflicts of interest for the “First Buddy," whose companies operate in heavily regulated industries and benefit from government spending and incentives.

And Trump’s response remains the same: Musk knows to avoid conflicts. “First of all he wouldn’t do it," Trump told reporters Thursday. “And second of all, we’re not going to let him do anything where there’s a conflict of interest."

Trump added that he is personally checking Musk’s work to make sure there aren’t conflicts.

Democrats aren’t so confident.

“Given the scale of your power to carry out sweeping administrative policies and your vast personal financial interests, the American people deserve to know how you stand to profit from your role in the Trump Administration," several Democratic members of the Senate and House wrote in a letter this past week calling on Musk to be more transparent.

The demands of the minority party came just days after Musk stood in the Oval Office, telling reporters his work was open for public scrutiny. “I fully expect to be scrutinized and get…a daily proctology exam," he said Tuesday. “It’s not like I think I can get away with something."

The letter asking for more transparency comes as Musk questions Democrats’ motivations for criticisms of DOGE cuts.

“The louder that any given politician yells about cutting government waste, the more corrupt they are," Musk posted. “Good rule of thumb."

When it was noted on X that Musk wore a black “Make America Great Again" hat during his Oval Office appearance in apparent violation of the Hatch Act, a federal law that limits political activities of federal employees, a supporter responded with a meme involving a pacifier and the message: “Shhhhh…Here’s your binky."

To which Musk replied with one of his favorites: a laughing tears emoji.

The question of Trump’s power to go through with Musk’s proposed cuts is at the center of a growing political and legal fight. As judges pause the administration’s actions, Musk has lashed out to his more than 200 million X followers. “We are witnessing an attempted coup of American democracy by radical left activists posing as judges!" Musk posted.

It is the kind of tactics he has used in business, too, when objecting to a Delaware judge who has upheld a ruling that struck down his massive, multibillion-dollar pay package. Musk is still fuming as Tesla appeals and encouraging other companies to relocate their incorporations to different jurisdictions.

As Musk has dug into Washington, his DOGE team has involved itself in areas of government that affect his companies, such a pushing to abolish the Consumer Financial Protection Bureau, which would scrutinize efforts by his X social network to enter financial payments; and the Federal Aviation Administration, which has tussled with SpaceX’s launches.

Protesters rally outside the Consumer Financial Protection Bureau on Monday.

On Thursday, Musk welcomed India Prime Minister Narendra Modi ahead of his visit with Trump. It was a meeting that had the trappings of two heads of states greeting each other with Musk’s young children sitting across from Modi’s entourage. Several of Musk’s companies have had business issues pending in India.

Later, Trump was asked if Musk was meeting Modi as a representative of the U.S. government or as a CEO. “I assume he wants to do business in India," Trump said.

Conservatives in general have rallied to support Musk as unassailable, often suggesting that he is unimpeachable because of his wealth, estimated at around $400 billion. They note Musk personally campaigned for Trump on the commitment of helping slash the government.

“He’s so rich, he’s so removed from the potential financial influence of it," Chris Sununu, the former Republican governor of New Hampshire, told CNN late last year

Influential podcaster Joe Rogan, an ally of Musk, said something similar this past week, dismissing concerns being raised about Musk’s intentions.

“He has $400 billion, I’m telling you, he’s not going to steal your money—that’s not what he’s doing," Rogan said. “He’s a super genius that has been f—ed with, OK, and when you’ve been f—ed with by these nitwits that hide behind three-letter agencies, and you’re dealing with one of the smartest people alive and he helps Donald Trump get into office and he goes, ‘I want to find out what kind of corruption is really around.’"

Among the lawsuits challenging Trump’s actions, is one filed by 14 state attorneys general looking to stop Musk, claiming the president has “delegated virtually unchecked authority" to him without Congress’s authorization and “meaningful" supervision.

Early Friday, Musk responded: “I’m just a volunteer tech support guy and have the T-shirt to prove it."

Write to Tim Higgins at tim.higgins@wsj.com