Congressional Republicans, egged on by Elon Musk and other top allies of President Trump, are escalating calls to remove federal judges who stand in the way of administration efforts to overhaul the government.

The outcry is threatening yet another assault on the constitutional guardrails that constrain the executive branch.

Judicial impeachments are rare and notoriously time-consuming. The mounting calls for removing federal judges, who already face increasing security threats, have so far not gained much traction with congressional leaders. Any such move would be all but certain to fail in the Senate, where a two-thirds majority would be needed for a conviction.

But even the suggestion represents another extraordinary attempt by Republicans to breach the foundational separation of powers barrier as Trump allies seek to exert iron-fisted control over the full apparatus of government. And Democrats charge that it is designed to intimidate federal judges from issuing rulings that may go against Mr. Trump’s wishes.

“The only way to restore rule of the people in America is to impeach judges,” Mr. Musk wrote this week on X, his social media platform, in one of multiple posts demanding that uncooperative federal judges be ousted from their lifetime seats on the bench.

“We must impeach to save democracy,” Mr. Musk said in another entry on X after a series of rulings slowed the Trump administration’s moves to halt congressionally approved spending cuts and conduct mass firings of executive branch workers. He pointed to a purge of judges by the right-wing government in El Salvador as part of the successful effort to assert control over the government there.