Originally Published: 05 MAY 21 11:15 ET

Updated: 05 MAY 21 12:07 ET

By Gabby Orr and Lauren Fox, CNN

(CNN) -- Former President Donald Trump is weighing in on the fight to replace Rep. Liz Cheney in the House Republican Party's leadership, blasting Cheney, endorsing her possible replacement and staying in touch with Republicans on Capitol Hill as the effort gets underway.

On Wednesday, Trump publicly backed Republican Rep. Elise Stefanik of New York to replace Cheney, releasing a statement saying the congresswoman "is a far superior choice, and she has my COMPLETE and TOTAL Endorsement for GOP Conference Chair."

Stefanik embraced Trump's endorsement in a Tweet.

"Thank you President Trump for your 100% support for House GOP Conference Chair. We are unified and focused on FIRING PELOSI & WINNING in 2022!" she wrote.

House Minority Leader Kevin McCarthy has been in contact with Trump about the mounting effort to oust Cheney from the No. 3 leadership position as GOP conference chairwoman, according to senior Trump adviser Jason Miller.

"They've definitely spoken recently ... within the last couple of days for sure," Miller, who spent last weekend with Trump at his Mar-a-Lago club, told CNN in a text message late Tuesday evening.

"They may have even spoken today," he added.

A second source confirmed to CNN that McCarthy and Trump had been in touch.

In a new statement Wednesday, Trump called Cheney a "warmonger" "who has virtually no support left in the Great State of Wyoming."

Though McCarthy's relationship with Trump remains strained after he stood by Cheney following her vote to impeach Trump earlier this year, the top House Republican has been working to repair the relationship with a visit to Mar-a-Lago in late January and frequent outreach to the ex-president and his team. Despite supporting McCarthy's push to dump Cheney from the GOP's leadership ranks, one person close to the former president said Trump was still bitter over the California Republican's initial support for Cheney and suggested it would take some time for the relationship between both men to fully heal.

"McCarthy made his choice. He chose Cheney over Trump and he chose business as usual over draining the swamp," this person said.

In recent days, however, McCarthy and Trump have worked together in an effort to boost Stefanik's campaign to be the new conference chairwoman.

Trump has long been a fan of Stefanik, who is angling to replace Cheney if she fails to survive a potential vote of confidence when House Republicans reconvene for their next conference-wide meeting, which could come as soon as May 12.

McCarthy has been privately supporting Stefanik to replace Cheney, and the No. 2 member of House Republican leadership, Rep. Steve Scalise of Louisiana, publicly endorsed Stefanik's bid for the job on Tuesday.

Two sources familiar with Cheney's conversations with members told CNN that she feels at peace with where she has stood on the election, on the January 6th deadly riot at the Capitol and her comments about Trump. Her calculation is that it is not worth trying to keep the leadership position if it requires lying about the election or the events that transpired leading up to January.

Cheney and Trump have had a roiling, public feud that significantly escalated in January when the Wyoming Republican voted to impeach the former President for his role in inciting the January 6 riot.

Despite a backlash from Trump's supporters in the conference, Cheney overwhelmingly kept her leadership position in a secret ballot vote 145-61 in February, and McCarthy gave a speech in support of the Wyoming Republican at the time.

But that relationship appears to have soured, as McCarthy has downplayed Trump's role in the insurrection and worked to rebuild his relationship to Mar-a-Lago. At the same time, Cheney has stood by her impeachment vote and blasted colleagues across Congress who supported efforts to challenge the election results.

Those simmering tensions boiled over this week, when McCarthy told Fox News on Tuesday morning that Cheney was failing to "carry out the message" of her conference, and Axios later reported that the California Republican was caught on a hot mic telling the Fox News host off air "I've had it with her."

"He literally saved her last time, and she doesn't even acknowledge it," a Republican lawmaker told CNN late last week, referring to a speech the GOP leader delivered at the February closed-door conference meeting.

The conference meets in full for the first time next week. At that point, McCarthy can call for a vote. If McCarthy doesn't go that route, then there are special procedures in place to ultimately force another vote, but those steps can take weeks to play out.

The vote will be conducted by secret ballot and can be approved by a simple majority of the full House GOP Conference, according to multiple GOP sources with knowledge of the process. That makes it almost certain that Cheney will lack the support to hang on to her No. 3 post.

If a rank-and-file member tried to suspend the rules and force a vote, that would require the backing of two-thirds of the 212-member conference to approve such a motion.

But with the backing of McCarthy, and under the procedures they plan to use, a simple majority would be enough to oust her and replace her — almost certainly with Stefanik, who has coalesced the conference behind her.

This story and headline have been updated with additional developments Wednesday.