Hard-right House Republicans have a new project — impeaching federal judges who have questioned President Donald Trump’s powers — and it’s quickly turning into the latest headache for Speaker Mike Johnson.

The push to remove jurists who have sought to halt Trump’s firings of federal employees, access to sensitive government systems and deportations of alleged foreign gang members has virtually no chance of succeeding, given the 67-vote requirement in the Senate for removal.

But it is nonetheless quickly turning into a major distraction for House GOP leaders after Trump himself called on social media Tuesday for the Washington-based judge who ordered the grounding of some deportation flights to be “IMPEACHED!!!” It threatens to sap political capital and antagonize key GOP blocs just as Johnson is hoping to put Trump’s sweeping domestic policy agenda into overdrive.

Rep. Brandon Gill of Texas, a conservative hard-liner, quickly followed through on Trump’s call, filing a measure to remove U.S. District Judge James Boasberg for seeking to “prioritize political gain over the duty of impartiality owed to the public.”

Impeachment proceedings, even when they don’t involve presidents, can be time- and resource-intensive affairs. Boasberg, who was nominated by President Barack Obama, is the fourth federal trial judge this year to be targeted with an impeachment filing from a congressional Republican after ruling against the Trump administration. But his is the first to draw backing from Trump.

Publicly, key GOP leaders are not closing the door on potential impeachments.

“Everything is on the table,” said Russell Dye, a spokesperson for House Judiciary Chair Jim Jordan (R-Ohio), who would oversee impeachment proceedings. A Johnson spokesperson said judges “with political agendas pose a significant threat” and that the speaker “looks forward to working with the Judiciary Committee as they review all available options under the Constitution to address this urgent matter.”

But privately there is dread inside Johnson’s leadership circle about the prospect of having to pursue messy, certain-to-fail impeachments that could ultimately backfire on the GOP’s razor-thin majority.

“It’s never going to happen,” said a senior House Republican aide. “There aren’t the votes.”

“It would be such a heavy lift and we’ve got too many heavy lifts coming up,” said another top GOP aide. “What is the endgame here?”

A third said GOP leaders and even some conservative House members are “rolling their eyes” at the impeachment filings that “aren’t going to go anywhere.”

The decision on how hard to push will ultimately fall to Johnson, a former constitutional lawyer who has so far resisted the hard-liners’ push to wage what many within his own leadership circle view as an unprecedented and wide-reaching congressional assault on the courts.

But Trump’s intervention this time could change that calculation — even as he stares down a punishing self-imposed deadline for advancing a massive tax, energy and border policy package before his members leave Washington next month for the Easter and Passover break. Johnson is heavily reliant on Trump to maintain his tenuous control over his fractious conference, and senior Republicans believe the speaker will likely need to offer some sort of concession to serve as a release valve as pressure builds on the MAGA right.

Fellow hard-liners cheered Gill on Tuesday, but there were signs of discomfort elsewhere in the House GOP.

“I don’t support it,” said Rep. Don Bacon (R-Neb.). “If their behavior was criminal, that is different.”

“I do not support impeaching a sitting judge based solely on a decision with which I disagree,” said another House GOP lawmaker, granted anonymity to speak candidly, who nevertheless agreed that Boasberg had “overstepped his authority” in ordering the halt to deportations under the 1798 Alien Enemies Act.

Both members echoed Chief Justice John Roberts in arguing that the courts, not Congress, were the proper place for Trump to address an adverse ruling.

Outside of the House, there appears to be even less of an appetite for impeachment.

In the Senate, which would be required to take up any impeachment as soon as articles come over from the House, Republicans have previously greeted the idea with disdain.

“Idiotic,” said Sen. John Kennedy (R-La.) when asked about the proposed judicial impeachments earlier this month, before Trump weighed in.

“You don’t impeach judges who make decisions you disagree with, because that happens all the time,” Sen. John Cornyn (R-Texas) said around the same time. “What you do is you appeal, and if you’re right, then you’re going to win on appeal.”

Both men sit on the Senate Judiciary Committee, whose chair, Chuck Grassley (R-Iowa), has spoken out about the need to “solve the problem of judicial overreach,” citing trial court orders that have national impacts, but has not commented on the calls for impeachments.

Some conservative lawyers with close ties to the administration have also warned against such a confrontation with the judiciary.

“Unpopular opinion: No judge will be impeached in connection with activist unconstitutional TRO’s & injunctions against the Trump Administration,” attorney Ron Coleman, a former law partner of Trump White House Counsel David Warrington, wrote on X amid a prior flurry of impeachment talk. “Strategically the Administration would be insane to try.”

Coleman stood his ground Tuesday, saying he supports Roberts’ statement urging politicians not to impeach judges over their rulings.

Despite Trump’s public posting Tuesday, it remains unclear just how hard he will push for impeachments of Boasberg or any other judges who have questioned his powers. Multiple Republicans close to the issue on the Hill say that Trump has not urged them to impeach anyone. But that could change if judges continue to hand down unfavorable rulings.

A small faction of Trump’s most diehard Hill supporters have been railing against the judiciary for weeks already — and are likely to keep the heat on Johnson to move forward.

While there is wide skepticism about the impeachment efforts — some Republicans have privately noted errors in some of the articles already filed — there are more serious talks among conservatives about trying to block funding for lower-level courts.

“They’re activists trying to stifle his agenda … radical left-leaning nutjobs in black robes trying to stop Trump,” said Rep. Troy Nehls (R-Texas), adding that lawmakers need to “send a message” even if the impeachments don’t ultimately succeed.

Roberts’ decision to speak out Tuesday only emboldened the GOP’s right flank, which has never been especially fond of the George W. Bush–nominated chief justice.

“Respectfully, Mr. Chief Justice, both James Madison and Thomas Jefferson disagree with you. So does the Constitution,” read an X posting from Rep. Andy Ogles (R-Tenn.), who filed impeachment articles against two federal judges last month.

“We are going to keep the impeachments coming,” Ogles added.

Kyle Cheney, Hailey Fuchs and Josh Gerstein contributed to this report.