House Republicans will gather Wednesday afternoon for a conference meeting that comes as two of its members are in hot water for very different reasons, and they could face threats to their futures in the party

Debate is expected at the meeting about the standing in the conference of Reps. Liz Cheney, R-Wyo., and Marjorie Taylor Greene, R-Ga. Cheney angered many of her fellow Republicans with a vote to impeach former President Trump, triggering a push by some of the Trump loyalists in the conference to remove her as the conference chair. 

And intense focus is on Minority Leader Kevin McCarthy, R-Calif., over Greene. The GOP leader Tuesday had his long-awaited, in-person talk with Greene – who's shown little if any remorse for previously espousing conspiracy theories.

Democrats are moving to potentially strip Greene of her committee assignments if McCarthy doesn't. That will be a topic of discussion in a separate Rules Committee meeting Wednesday. But some Republicans have alleged a double standard given past anti-Semitic affiliations of Rep. Ilhan Omar, D-Minn., and inciteful words from Rep. Maxine Waters, D-Calif. A group of Republicans moved to strip Omar of her committee assignments Tuesday. 

Rep. Liz Cheney, R-Wyo., is under fire for her impeachment vote, and a number of House Republicans are supporting an effort to oust her as the GOP conference chair. (William B. Plowman/NBC/NBC NewsWire via Getty Images)

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Politico reported Wednesday that McCarthy would try to work out a deal with House Majority Leader Steny Hoyer, D-Md., to get Democrats to back off a vote to remove Greene from committees, which would place House GOP members in a painful political position. But according to a statement from Hoyer Wednesday, nothing came of their conversation and the House will vote to strip Greene of her committee assignments Thursday. 

Responding to earlier reports that McCarthy might have been considering removing her from at least one committee to preempt a House vote, Greene said in a tweet: "No matter what @GOPLeader does it would never be enough for the hate America Democrats."

The movement to remove Cheney as the GOP conference chair is spearheaded by Rep. Matt Gaetz, R-Fla., who traveled to Wyoming last week to hold a political rally against Cheney. 

"We are in a battle for the soul of the Republican party and I intend to win it," Gaetz said. He was joined by phone by Donald Trump Jr., who said "it's time to have a change at the top." 

Cheney is backed by a number of other members of the conference, however, including Reps. Dan Crenshaw, R-Texas; Nicole Malliotakis, R-N.Y.; Chip Roy, R-Colo., and Tom Cole, R-Okla. She also received tepid support from McCarthy. 

But more recently, some powerful Senate voices have backed Cheney, led by Senate Minority Leader Mitch McConnell, R-Ky., who usually does not insert himself into House affairs. 

"Liz Cheney is a leader with deep convictions and the courage to act on them. She is an important leader in our party and in our nation. I am grateful for her service and look forward to continuing to work with her on the crucial issues facing our nation," McConnell said in a statement Monday. 

U.S. Rep. Matt Gaetz, R-Fla., grabs the hand of a supporter following a rally against U.S. Rep. Liz Cheney, R-Wyo., Thursday, Jan. 28, 2021, outside the Wyoming State Capitol in Cheyenne. Gaetz spoke to hundreds, bashing Cheney after she voted to impeach former President Donald Trump for his role in the Jan. 6 insurrection at the U.S. Capitol, and he called for a group effort in finding the right nominee to replace her when she is up for reelection in 2022. (Michael Cummo/The Wyoming Tribune Eagle via AP)

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McConnell has made clear his disdain for Trump after the former president's post-election behavior. But one of the senators who's been most involved in Trump's impeachment defense also backed Cheney. 

"I believe @RepLizCheney is one of the strongest and most reliable conservative voices in the Republican Party," Sen. Lindsey Graham, R-S.C., said. "She is a fiscal and social conservative, and no one works harder to ensure that our military is well prepared."

He added: "Liz knows that a strong America is a safe America. She believes we must confront radical Islam and take the fight to them to ensure there are no more 9/11’s. In the eyes of many – Liz Cheney’s experience, leadership, and strength are invaluable to the Republican Party."

The Republicans who are upset at Cheney over her impeachment vote said that her stance against Trump – who she said "summoned this mob, assembled the mob, and lit the flame of this attack" – means she's out of touch with the majority of the House GOP conference, which is still loyal to the twice-impeached former president. 

"When Rep. Cheney came out for impeachment today, she failed to consult with the conference, failed to abide by the spirit of the rules of the Republican Conference, and ignored the preferences of Republican voters," Rep. Matt Rosendale, R-Mont., who was among the first to call for her ouster as conference chair, said. "She is weakening our conference at a key moment for personal political gain and is unfit to lead."

There's expected to be major disagreements at the Wednesday conference over what to do about Cheney, who has been working the phones to whip support, multiple sources tell Fox News. 

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They add that Cheney will likely make her case at the meeting but is not expected to apologize for her impeachment vote. Instead, she’s expected to talk about the future of the Republican Party.

Meanwhile, it's likely there will also be a discussion about Greene's future in the House GOP.

House Republicans have been largely silent on Greene, including and especially the leadership. Asked if any decisions were made at a House GOP Steering Committee meeting Tuesday night, Minority Whip Rep. Steve Scalise, R-La., said "No, we're still going to be working through some things."

But some Senate Republicans this week, as they threw their support behind Cheney, also condemned Greene, citing past conspiratorial comments. 

"Somebody who’s suggested that perhaps no airplane hit the Pentagon on 9/11, that horrifying school shootings were pre-staged, and that the Clintons crashed JFK Jr.’s airplane is not living in reality," McConnell said Monday. "This has nothing to do with the challenges facing American families or the robust debates on substance that can strengthen our party."

Former President Trump and House Minority Leader Kevin McCarthy, R-Calif., meet at Mar-a-lago Thursday. (Save America PAC)

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Senate Republican Conference Chair John Barrasso of Wyoming, who has defended Cheney, on Tuesday compared Greene to former Rep. Steve King, R-Iowa, who the House GOP stripped of committee assignments over racist statements.

"I think our party has to make it very clear that she does not represent us in any way. Our big tent is not large enough to both accommodate conservatives and kooks," Sen. Mitt Romney, R-Utah, also said. 

What likely won't happen Wednesday is a vote to remove Cheney as the conference chair, which would require a petition that she step down with 20% of the conference – or 43 members – signed on to be submitted at the meeting. Then, it would require a two-thirds vote to suspend the rules – or McCarthy's support – to get to an up-or-down vote on a resolution that Cheney step down. 

Instead, it will probably be a longer process with a petition calling for a special conference meeting to consider such a resolution, with the same requirements, submitted after Wednesday. House conservatives say that they have well over 100 members willing to remove Cheney as conference chair. 

If those circulating the petition against Cheney do get the requisite number of signatures, then the petition must be granted within 10 legislative days. At that meeting, the resolution could be either voted on immediately with two-thirds support or with McCarthy's support, or it would be sent to a committee. That committee would later report the resolution with a favorable or unfavorable recommendation, which could then be passed by a simple majority vote. 

Senate Minority Leader Mitch McConnell (R-Ky.) heads to the Senate floor before being called into session on Jan. 26, 2021, in Washington, D.C. McConnell made two unusual forays into House affairs this week with statements supporting Rep. Liz Cheney, R-Wyo., and condemning Rep. Marjorie Taylor Greene, R-Ga., as a person "not living in reality." (Samuel Corum/Getty Images)

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The resolution would be that Cheney should step down as the leader of the conference, not to actually remove her, so it would not actually have force. But it is not expected that Cheney would attempt to remain conference chair if the resolution passes. 

Trump Jr. indicated at the Thursday rally that those interested in ousting Cheney may take their time in this process, warning that if too many Trump-supporting congressmen run for Cheney's spot, she could keep her seat with the support of less than half of the conference. 

"Let's find exactly the opposite of her, and let's back that person fully," Trump Jr. said at the Gaetz rally. "But let's not make that decision today. We have some time. Let's find the right one, let's not split this vote up and blow our opportunity to get rid of a RINO." 

What Republicans do about Cheney and Greene may also indicate the path it will take in the post-Trump era. 

Donald Trump Jr. waits for President Donald Trump and first lady Melania Trump to arrive and board Air Force One for a final time at Andrews Air Force Base, Md., Wednesday, Jan. 20, 2021. Trump Jr. last week joined a rally against Rep. Liz Cheney, R-Wyo., by phone. (AP Photo/Manuel Balce Ceneta)

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Some members still want to hold tightly to the former president, who has indicated that he will fuel primary challenges to any members he sees as insufficiently loyal to him. That fear of a primary challenge, plus Trump's loyal base, may guide many members' actions, just as it did during Trump's presidency. 

But others worry that if the GOP accepts Greene while rebuking Cheney, it may keep the Trump base happy at the expense of its morality and any hope of winning moderates in future elections. 

"I think we should have nothing to do with Marjorie Taylor Greene, and think we should repudiate the things she said and move away from her," Romney said. 

Fox News' Kelly Phares, Chad Pergram, Jason Donner, Mike Emanuel and Paul Steinhauser contributed to this report.