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After years of encouraging Democrats and voters to take a meritocratic approach when evaluating candidates for office, Republicans are coming under fire for insisting that ousted House GOP Conference Chair Liz Cheney must be replaced by another woman.

Before the Wyoming congresswoman was booted from her leadership post in a vote on Wednesday, House Republicans had sent out clear signals that her successor would need to be a woman. Male members who had reportedly been interested in the role, such as Republican Study Committee Chairman Jim Banks of Indiana, were quickly dismissed as the names of three women – Reps. Elise Stefanik of New York, Ann Wagner of Missouri and Jackie Walorksi of Indiana – were circulated inside the conference.

Soon, party leaders settled on Stefanik, a millennial congresswoman whose profile rose in late 2019 amid her fervent defense of then-President Donald Trump during his first impeachment inquiry.

Born out of what leadership saw as a political necessity given the party’s precarious position with women voters, Stefanik was quickly elevated as Cheney’s presumptive replacement. Even in conversations between House Minority Leader Kevin McCarthy and Trump, who vowed to recruit a primary challenger against Cheney after she voted to impeach him in his second inquiry earlier this year, Stefanik was identified early on as a suitable replacement, according to two people familiar with their discussions. The former President eventually offered a public endorsement, describing Stefanik as a “gifted communicator” in a statement on Monday.

“They thought it was going to do damage in the media if they tapped a man for the job,” said one top Trump ally, describing discussions that occurred around Cheney’s ouster between the former President and House Republicans.

Instead, the hurried push to install Stefanik as GOP chair – a vote that is expected to come on Friday – has begun to backfire. Conservatives both on and off Capitol Hill are raising questions about prioritizing optics – in this case, preventing the party from having three men occupy its House leadership ranks – over ideological consistency.

“We’re almost at the anniversary of Joe Biden saying he needs to pick a woman as a running mate. This is what the Democrats always do and I’m against it,” said the top Trump ally.

“No GOP woman cares about identity politics!” added conservative commentator Ann Coulter in a tweet Wednesday afternoon.

In a column posted shortly after Cheney was removed from her post on Wednesday, the Washington Post’s Jennifer Rubin contended that the “most obvious reason” Republicans had settled on Stefanik, whose voting record has raised eyebrows among the party’s most conservative members, “is because the party – though it supposedly abhors identity politics – needs a skirt to hide behind as it jettisons a strong, independent-minded female colleague.”

One House GOP staffer agreed with Rubin’s assessment. The anointing of Stefanik, this staffer said, represented “rank hypocrisy” inside the party, noting that Republicans have often cast quotas that are aimed at addressing gender diversity inside American companies, presidential Cabinets, and other institutions as pandering or empty symbolism.

“This is what we claim to despise and yet here we are saying, ‘We can’t consider these other candidates, who are more attuned to what our constituents want, because they are men,’ ” the staffer said.

Top Democrats have also seized on the GOP’s push to swap Stefanik in for Cheney. In a faux “help wanted” ad released by House Speaker Nancy Pelosi last Tuesday, the California Democrat accused Republican leaders McCarthy and House Minority Whip Steve Scalise of seeking to replace Cheney with “a woman who isn’t a ‘threat’ to them.”

To be sure, not every House Republican has supported the Stefanik-for-Cheney leadership swap. Some have said the contest to replace Cheney would benefit from having multiple contenders, while others have shown little appetite for slotting another woman in the role to shield the party from criticism.

“I ask myself every day why Jim Jordan isn’t on our leadership team,” Rep. Brian Mast of Florida told CNN earlier Wednesday, signaling that he would be open to seeing others inside the conference fill the No. 3 leadership position.

Efforts to coronate Stefanik as incoming conference chair come as the GOP finds itself in perilous territory with female voters, who contributed to the Democratic Party’s suburban gains in the 2020 election and could stymie Republican hopes of retaking the House next fall if the relationship remains strained. Republicans need to flip at least five seats to take over the lower chamber, and some worry that Cheney’s orchestrated removal from leadership will further alienate women right as the party is ramping up for its critical midterm push.

But insider efforts to preempt such consequences by promoting another woman to the leadership role may have also underscored the risks of so-called identity politics, if the reaction to Stefanik among conservative House Republicans is any indication.

In a scathing letter sent to colleagues on Tuesday, Rep. Chip Roy of Texas said Stefanik’s voting record “embodies much of what led to the 2018 ass-kicking we received by Democrats” and urged Republicans to consider leaving the position of conference chair open if the party can’t coalesce behind “someone who reflects our conservative values.” Roy and other conservative skeptics have cited Stefanik’s votes against the House GOP’s 2017 Tax Cuts and Jobs Act and the Trump administration’s request to use emergency funds for border wall construction as red flags. They have also pointed to her sharp criticism of Trump over his withdrawal from the Paris Climate Agreement and rhetoric on trade.

“The lack of any challenger doesn’t remove any questions I have about her voting record and whether her positions are going to interfere with our ability to look to message for the conference,” Rep. Ben Cline of Virginia, a member of the House Freedom Caucus, where Stefanik’s voting record and past criticism of Trump has become a source of consternation in recent days, told CNN on Wednesday.

Roy, a Freedom Caucus member himself, was said to be considering an official bid for the job as of Wednesday afternoon, with his spokesperson telling reporters, “If the position must be filed, then this must be a contested race – not a coronation.” It is not yet clear if his candidacy would pose a significant threat to Stefanik, who has privately suggested she would only serve in the role through 2022 and has already received the backing of McCarthy, Trump and Scalise, the second-ranking House Republican.

Despite publicly backing of Stefanik, McCarthy said late Wednesday that he held off on holding a vote for his colleague immediately after Cheney’s ouster because “competition is good.”

Former Republican Rep. Deborah Pryce of Ohio, who became the first woman to occupy the role of conference chair when she was elected to the position in 2003, had mixed feelings about the push to replace Cheney with a woman. Pryce, who described Cheney’s ousting in an interview with CNN as “very unfortunate,” said she was pleased that Republicans are likely to maintain female representation in their leadership ranks if Stefanik is voted into the role.

But she and others added that there is a potential downside to installing another woman in the No. 3 position for the third consecutive time, following Cheney and Rep. Cathy McMorris Rodgers of Washington, who held the title of GOP conference chair from January 2013 through January 2019.

“I think Elise will do a great job … but it isn’t, it shouldn’t be, and I hope it never becomes the token slot for women in leadership,” Pryce said.

Though Republicans made significant strides in the last election to add women to their congressional minority – including with the help of Stefanik, whose leadership PAC gave $415,000 to Republican candidates in 2020 – the party still pales behind Democrats in female representation. A study by the Pew Research Center released earlier this year found that 38% of Democrats in the 117th Congress are women, versus 14% of Republicans. A Republican woman has also never served as party whip or House Speaker.

For her part, Stefanik said Wednesday she “absolutely” has enough support inside the conference to clinch the spot after speaking directly with some of the conservative House members who raised concerns about her candidacy earlier this week.

“We have great support conference-wide, from members of the Freedom Caucus to the Tuesday Group,” she said.

CNN’s Simone Pathe contributed to this story.