CNN  — 

GOP leaders are facing growing pressure from conservative hardliners to put their political muscle behind a primary challenge seeking to oust Rep. Liz Cheney, a move that puts top Republicans in an awkward spot as they try to avoid intraparty fights and the ire of Donald Trump in their quest to take back the majority.

House Minority Leader Kevin McCarthy has so far been successful in tamping down calls to expel Cheney and Rep. Adam Kinzinger from the GOP conference, arguing it’s an unnecessary distraction at a time when Republicans are poised to win back the House. McCarthy has also privately reasoned to members that Kinzinger is retiring anyway and Cheney could be knocked out in her primary this summer, according to members who have spoken to the leader.

GOP leaders in the House have long had a posture of neutrality in primaries, so jumping behind Cheney’s challenger would amount to a breach of protocol, prompt internal turmoil and cause a major distraction as the party wants to keep its focus squarely on Democratic pickup opportunities. But staying quiet could open McCarthy up to criticism from Trump and his staunchest allies – as they got a big boost Friday when the Republican National Committee censured Kinzinger and Cheney for their roles on the January 6 select committee. That unprecedented rebuke came in addition to steps the committee took earlier this week to enable the RNC to back a Cheney challenger.

“That’s the question that everyone should pay attention to: If Kevin McCarthy does go against Liz Cheney,” said Rep. Marjorie Taylor Greene, a far-right Georgia Republican and one of Trump’s closest allies. “That’s the inside baseball that people should be watching.”

On Friday, McCarthy repeatedly refused to answer any questions when asked about the RNC resolution and whether he would get behind Cheney’s primary challenger, Harriet Hageman.

The discussion about how to handle Cheney and Kinzinger recently made its way to McCarthy’s office. Behind closed doors, the GOP leader met with members of the hardline House Freedom Caucus, which had been agitating for months to kick Cheney and Kinzinger out of the GOP conference, something that requires a two-thirds majority.

Emerging from the meeting, the Cheney critics seemed to have shifted course, indicating they instead would focus their fight on trying to take out Cheney in her primary.

“We are all on the same page,” said Rep. Scott Perry, a Pennsylvania Republican who chairs the group. Another House Freedom Caucus member told CNN: “there are shared objectives” with the leadership.

Greene added: “I’m actually more interested in the long game. It’d be far more insulting to me to kick them out of the conference, and then see Liz Cheney win her reelection and come back to Congress. The plan I’m most invested in is making sure she loses and she can never come back.”

‘We don’t play in primaries’

Yet it’s far from clear what the GOP leadership will do – if anything – to oust Cheney back home in her primary.

The House GOP’s campaign arm has an official policy of not getting involved in primaries, while Republican leaders also don’t typically wade into those races – a risky move that could backfire if the targeted lawmaker ends up winning. Not to mention, McCarthy is more worried about focusing his energy on races that actually matter for the majority; Wyoming is a ruby red state and whoever wins the primary is expected to sail to victory in the general election.

“We don’t play in primaries,” Rep. Tom Emmer of Minnesota, the chairman of the National Republican Congressional Committee, told CNN. “We’re not involved in any of that.”

Rep. Steve Scalise, the No. 2 House Republican, said he wasn’t involved in primaries – and then shifted to an attack on the White House.

Initially, the RNC resolution was going to call for Kinzinger and Cheney to be expelled, which would have put even more pressure on McCarthy to act, but it was watered down to a censure resolution.

For McCarthy to stay in Trump’s good graces, he can’t be seen as too sympathetic or even ambivalent toward Cheney, or else he risks incurring the wrath of Trump and the right – a crucial voting bloc in his bid to become speaker. And he’s already defended her on two occasions: he stood up for Cheney during the first effort to boot her from leadership immediately after she voted to impeach Trump last year for inciting the deadly attack on the Capitol, and he has more recently resisted the demands to remove her and Kinzinger from the conference.

But if McCarthy engages to take out a GOP member, he’s bound to upset a number of his more moderate members who want to keep focused on taking down Democrats.

“Not going to be helpful,” said Rep. Fred Upton, a veteran Michigan Republican who voted to impeach Trump last year. Upton told CNN on Friday he still hasn’t decided whether he will run for reelection. And he also objected to the RNC move to punish his two colleagues.

“We’re trying to expand the base,” Upton said. “This doesn’t help us. Just doesn’t work.”

Other like-minded Republicans agreed.

Rep. Dan Newhouse, a Washington state Republican who also voted to impeach Trump for inciting the Capitol attack, said: “I would hate to see that happen,” referring to GOP leaders potentially backing Cheney’s primary foe.

“This is a distraction that we shouldn’t be engaged in,” Newhouse said. “We should be focused on truly who our opponents are.”

“I don’t see how this is at all productive,” said Rep. Peter Meijer of Michigan, another one of the 10 impeachment backers and who is also facing a Trump-backed primary challenger, when asked about his GOP colleagues being targeted. “We are heading into a midterm where the wind seems to be at our back, the Democrats are doing everything they can to make the argument why they should no longer be trusted with the governing authority.”

Some Republicans avoided discussing the matter – such as Rep. Mariannette Miller-Meeks and Darrell Issa – who wouldn’t comment Friday.

And other Trump allies also suggested that the party should stay out of this fight.

“I think the party should try and continue to work with them,” said Texas Rep. Pete Sessions. “I think this is a fight between Donald Trump and (Kinzinger and Cheney), not the party.”

Trump allies apply pressure

Trump’s allies are still hoping to rope top Republicans into their revenge campaign in Wyoming, where Hageman has struggled to outraise the congresswoman.

Perry suggested the group’s political arm is likely to put its weight behind one of Cheney’s opponents: “I think you can extrapolate,” he said.

Meanwhile, Rep. Lauren Boebert of Colorado, another member of the Freedom Caucus and staunch Trump ally, said that when she starts wading into races, “that will probably be one I get involved in.”

Rep. Matt Gaetz of Florida, who flew to Wyoming to rally against Cheney last year, said he doesn’t think it matters whether the House GOP leadership gets involved in the race because Trump already has endorsed a candidate in the race.

“Leadership of our party is Donald Trump,” Gaetz said. “The leader of the Republican Party has endorsed the person that will win that race.”

While the Freedom Caucus is now training its fire on Cheney’s primary battle, ousting her from Congress won’t necessarily come easy, even in a state where Trump won with 70% of the vote. Cheney has ties to a powerful political dynasty and has excelled in the money race, bringing in a record-breaking $2 million last quarter, compared to Hageman’s $443,000. Former President George W. Bush was among Cheney’s donors.

And Sen. Mitt Romney of Utah is headlining a March fundraiser for Cheney, according to an invitation provided to CNN. Among those serving as hosts for the event are prominent Bush-era figures, such as Scooter Libby and Michael Chertoff, as well as her father, former Vice President Dick Cheney.

However, the money dynamic could change as election season heats up, especially now that the RNC has the ability to get involved. Hageman is also listed on the agenda for a fundraiser in Florida later this month benefiting a pro-Trump super PAC, and Trump has made Cheney the top focus on his revenge campaign against the House Republicans who voted to impeach him.

“This is further proof that Liz Cheney has completely lost her ability to be effective in Congress for the people of Wyoming,” Hageman said of the RNC resolution in a statement. “She doesn’t have allies in the Republican Party, and the Democrats only see her as a temporary and useful tool to achieve their partisan ends.”

Cheney, meanwhile, has expressed no regrets about her decision to impeach Trump and serve on the January 6 select committee, even as she continues to suffer consequences for her actions.

“If the price of being willing to tell the truth and get to the bottom of what happened on January 6, and make sure that those who are responsible are held accountable is a censure, then I am absolutely going to continue to stand up for what I know is right,” Cheney told CNN. “And I think that it is a sad day for the party of Lincoln that that’s where we are.”

CNN’s Morgan Rimmer contributed to this report.