WASHINGTON (AP) — House Minority Leader Kevin McCarthy faced unrest Tuesday from opposing ends of the Republican spectrum over Reps. Liz Cheney and Marjorie Taylor Greene, underscoring GOP fissures as the party seeks its pathway without Donald Trump in the White House.

Hard-right lawmakers were itching to oust Cheney, a traditional conservative and daughter of former Vice President Dick Cheney, from her post as the No. 3 House Republican after she voted to impeach Trump last month. Senate Minority Leader Mitch McConnell praised Cheney and aligned himself with party moderates trying to isolate or punish Greene, a first-term congresswoman gaining renown for embracing outlandish fictions like suggestions that mass school shootings were staged.

The looming decisions on Cheney, R-Wyo., and Greene, R-Ga., represent a moment of reckoning for a party struggling with its future. Two weeks after Trump left office, House Republicans are effectively deciding whether to prioritize the former president’s norm-shattering behavior and conspiracy theories and retain the loyalty of his voters over more establishment conservative values.

“At the very moment that Joe Biden is lurching to the left is the moment that the Republican Party is lurching out of existence,” GOP pollster Frank Luntz said of the new Democratic president, who is preparing to try muscling a mammoth COVID-19 relief package through the narrowly divided Congress.

“We can either become a fringe party that never wins elections or rebuild the big tent party of Reagan," Maryland Gov. Larry Hogan, one of the few elected Republicans who routinely rebuked Trump, said in a written statement. Without mentioning Cheney or Greene, he added, “I urge congressional Republicans to make the right choice.”

But pro-Trump forces in and out of Washington remain powerful. John Fredericks, who led Trump’s Virginia campaigns in 2016 and 2020, warned that there would be party primaries against Cheney defenders.

“We’ve got millions and millions of woke, motivated, America-first Trump voters that believe in the movement,” Fredericks said. “If you’re going to keep Liz Cheney in leadership, there’s no party.”

Rep. Matt Rosendale, R-Mont., a leader of the effort to oust Cheney, says he has enough support to succeed.

“She's brought this on herself,” Rosendale said. He said Cheney, who was joined by only nine other Republicans in backing impeachment, was wrong to not forewarn colleagues about her decision.

House Republicans planned a meeting for Wednesday, when Cheney’s fate as leader could be decided. McCarthy, R-Calif., was also expected to talk privately this week with Greene, and a House vote on a Democratic-led move to strip her of committee assignments could occur Wednesday.

Greene, who has suggested that school shootings in Newtown, Connecticut, and Parkland, Florida, could be hoaxes, was selected to serve on the House education and budget committees. Democrats told McCarthy this week that if he didn't remove Greene from her committees, the House would vote to do so, according to a person familiar with the conversation, who spoke on condition of anonymity to discuss internal conversations.

Republicans say that GOP members would unite against a Democratic move to remove Greene from her committee assignments and that such an effort would help Greene cast herself as a victim of partisan Democrats.

As if to illustrate that point, Greene herself tweeted fundraising appeals Tuesday that said, “With your support, the Democrat mob can’t cancel me,” beneath a picture of herself standing with Trump.

Democrats say they think some Republicans will support ousting Green from committees and that a House vote will make McCarthy look weak and further erode GOP support among moderate suburban voters.

The Democratic Congressional Campaign Committee launched a $500,000 ad campaign Tuesday aimed at eight Republicans, including McCarthy. The ads attempt to tie them to Greene and other adherents of QAnon, which focuses on the false belief that top Democrats are involved in child sex trafficking and cannibalism, with a narrator who says each targeted GOP lawmaker “stood with Trump and the lies.”

The handling of Greene and Cheney presented a tricky balancing act for McCarthy, whose aides did not return messages seeking comment.

Penalizing Cheney for what McConnell called a “vote of conscience” on impeachment would be awkward without also punishing Greene, who has used social media to show support for violence against Democrats and baseless QAnon pro-Trump conspiracy theories. Action against either risked angering the GOP's numerous Trump supporters or its more traditional conservative backers.

“You can’t do the normal political song and dance and appease this side slightly and appease that side slightly,” said former Rep. Mark Sanford, R-S.C., who lost a 2018 party primary after clashing with Trump. “The whole nature of the Trump phenomenon is there is no appeasement.”

McCarthy has said he supports Cheney but also has “concerns,” leaving his stance on her unclear.

McConnell, R-Ky., McCarthy's counterpart across the Capitol and Washington's most powerful Republican, weighed in this week to support Cheney and condemn Greene. McConnell called Cheney “a leader with deep convictions and courage,” and, without mentioning Greene's name, he called her “loony lies” a “cancer” on the GOP.

McConnell reiterated his remarks about Greene during a Senate GOP virtual lunch Tuesday and no one spoke up in her defense, according to a Republican who spoke on condition of anonymity to discuss the private call.

McConnell’s strong words could put pressure on McCarthy, who has been more cautious in his dealings with both lawmakers.

The guarded McConnell usually avoids delving into House affairs. His remarks suggest concerns about letting the GOP’s most pro-Trump, hardest-right factions gain too much sway in the party.

McConnell was not alone. Rep. Adam Kinzinger, R-Ill., who's been trying to combat the GOP's pro-Trump wing, said he favored removing Greene from her committees, saying Republicans must “take a stand to disavow” her.

Sen. Mitt Romney, R-Utah, a Trump critic and the GOP 2012 presidential nominee, said Republicans must “separate ourselves from the people that are the wacky weeds."

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Peoples reported from New York. AP Congressional Correspondent Lisa Mascaro contributed to this report from Washington.