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Rep. Elise Stefanik, the favorite to replace Rep. Liz Cheney as the House GOP conference chair, voted with former President Donald Trump less than Cheney and has lower voting scores from top conservative organizations. 

According to a tool on the FiveThirtyEight website on "Tracking Congress In The Age Of Trump," Cheney, R-Wyo., voted with Trump 92.9% of the time compared to 77.7% for Stefanik, R-N.Y.

The conservative group Heritage Action, meanwhile, gave Cheney a 91% score compared to just 56% for Stefanik during the most recent Congress. And the American Conservative Union, which hosted the extraordinarily pro-Trump Conservative Political Action Conference (CPAC) earlier this year, gives Cheney a 78% rating compared to just 44% for Stefanik. 

Stefanik, notably, lives in a more moderate district in New York than Cheney, who represents bright-red Wyoming. But Stefanik has still won by more than double-digits every election since 2014, when she first went to Congress. 

Rep. Liz Cheney, R-Wyo., the House Republican Conference chair, speaks with reporters following a GOP strategy session on Capitol Hill in Washington, Tuesday, April 20, 2021. (AP Photo/J. Scott Applewhite)

Rep. Liz Cheney, R-Wyo., the House Republican Conference chair, speaks with reporters following a GOP strategy session on Capitol Hill in Washington, Tuesday, April 20, 2021. (AP Photo/J. Scott Applewhite)

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Cheney, who has publicly feuded with Trump over the former president's false claims that the 2020 presidential election was stolen, faced a vote earlier this year to remove her from her post as the third-ranking Republican in the House.

She easily defeated that effort, but has continued to battle the former president's false claims even as other members of House GOP leadership, most notably Minority Leader Kevin McCarthy, R-Calif., have aimed to mend fences and ignore the issue. 

Momentum continued to build against Cheney as the divide between her and other Republicans became more stark at a House GOP policy retreat last week. And it reached a boiling point earlier this week when Trump called the 2020 election "Fraudulent" in a statement, prompting Cheney to hit back in a tweet. 

"The 2020 presidential election was not stolen," she said. "Anyone who claims it was is spreading THE BIG LIE, turning their back on the rule of law, and poisoning our democratic system." 

After that, more Republicans began to publicly call for Cheney's ouster and Stefanik eventually began making calls to build support for a potential challenge to Cheney. 

"Liz will have more to say in the coming days. This moment is about much more than a House leadership fight," Cheney spokesperson Jeremy Adler told Fox News Wedneday.

In this image from video, Rep. Elise Stefanik, R-N.Y., speaks as the House reconvenes to debate the objection to confirm the Electoral College vote from Arizona, after protesters stormed into the U.S. Capitol on Wednesday, Jan. 6, 2021. (House Television via AP)

In this image from video, Rep. Elise Stefanik, R-N.Y., speaks as the House reconvenes to debate the objection to confirm the Electoral College vote from Arizona, after protesters stormed into the U.S. Capitol on Wednesday, Jan. 6, 2021. (House Television via AP)

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Stefanik is highly popular in the Republican conference, as she has a history of helping raise money for other incumbents. She notably also helped a number of House freshman Republican women in the 2020 elections. 

Stefanik gained notoriety in the past few years as a fierce defender of Trump during the House impeachment hearings in the fall of 2019. She was eventually named the honorary New York chair of Trump's reelection campaign in early 2020, despite her voting record that didn't always align with the former president. 

But she's stood strongly with Trump in recent months, as the president repeated false claims that he won the presidential election and backed a barrage of failed lawsuits challenging the election results. 

Stefanik voted with most House Republicans against impeaching Trump for his alleged role in the Jan. 6 attack on the Capitol. 

Stefanik voted to object to Pennsylvania's Electoral College slate, but did not vote to object to Arizona's electors. Stefanik's office did not return a request for comment from Fox News for this story. 

Cheney objected to neither slate of electors and then voted to impeach Trump over the Jan. 6 attack. 

The reason many of Cheney's opponents cite for the fact she should no longer be the conference chair is that she is out of step with most rank-and-file Republicans. 

Former President Donald Trump walks on the South Lawn of the White House in Washington, Sunday, Nov. 29, 2020, after stepping off Marine One. The Republican Party has undergone a series of internal battles since Trump left office over what role he should play in the future of the party. (AP Photo/Patrick Semansky)

Former President Donald Trump walks on the South Lawn of the White House in Washington, Sunday, Nov. 29, 2020, after stepping off Marine One. The Republican Party has undergone a series of internal battles since Trump left office over what role he should play in the future of the party. (AP Photo/Patrick Semansky)

"Liz Cheney was put on notice when our conference held a vote to remove her in February," Rep. Lance Gooden, R-Texas, said in a statement. "Her role is to lead House Republican messaging, but she is totally unaligned with the majority of our party. We cannot fight for the America First agenda with her in a leadership position."

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But Gooden's 94.5% alignment with Trump, according to FiveThirtyEight, is far closer to Cheney's score than Stefanik's. Gooden, meanwhile, has a 100% score from Heritage and a 71% score from the American Conservative Union. 

Sen. Josh Hawley, R-Mo., told CNN that Cheney is "really out of step with GOP voters and members." Hawley has an 83% rating from Heritage, 78% from the American Conservative Union and voted with Trump 86.7% of the time, according to FiveThirtyEight. 

Others, however, said the increase in sentiment against Cheney was less about votes and more about messaging and Cheney's regular barbs against Trump. 

"There's no concern about how she voted on impeachment, that decision has been made. I have heard from members concerned about her ability to carry out the job as conference chair to carry out the message," McCarthy said on "Fox & Friends" Tuesday. "We all need to be working as one if we're able to win the majority. Remember, majorities are not given. They are earned. And that's about the message about going forward, combating Joe Biden."

McCarthy continued to say that Republicans should "all work together instead of attacking one another."

One source told Fox News, "She continues to raise issues with the former president" and added that "if you're out of sync with Trump," you're not in sync with the Republican conference.

Supporters of President Donald Trump climb the west wall of the the U.S. Capitol on Wednesday, Jan. 6, 2021, in Washington.

Supporters of President Donald Trump climb the west wall of the the U.S. Capitol on Wednesday, Jan. 6, 2021, in Washington. (AP Photo/Jose Luis Magana)

The role of conference chair, notably, is considered fundamentally a position with a focus on messaging. 

An aide for a moderate Senate Republican, meanwhile, told Fox News that it is unclear what Cheney's end game is as she continues to battle with Trump over the election. 

"It's sad to me because I really like Rep. Cheney," the aide told Fox News. "I wish she could have just made her point and moved on to fighting Democrats." 

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Others, however, are expressing their support for Cheney to remain the conference chair, including the Wall Street Journal editorial board and prominent conservative radio host Hugh Hewitt. 

"It'd be extremely short-sighted and self-destructive for@HouseGOP to move against the very smart @Liz_Cheney," Hewitt tweeted. "You don't win @HouseGOP maj by subtraction but by addition. Not sure this buzz is more than legacy media addiction to 'GOP civil war' narrative but if it is, big mistake."

"Mr. McCarthy knows Ms. Cheney is right. The election wasn't stolen, yet Mr. Trump wants an endorsement of his stolen claim to be a litmus test for every Republican candidate. He’s the one who wants to refight his losing campaign," the Journal wrote. 

Fox News' Chad Pergram, Jason Donner, Brooke Singman and Kelly Phares contributed to this report.