Pollster Frank Luntz: Trump's 'Big Lie' is working, may cost GOP votes

Veteran GOP pollster Frank Luntz warned that former President TrumpDonald TrumpTexas announces election audit in four counties after Trump demand Schumer sets Monday showdown on debt ceiling-government funding bill Pennsylvania AG sues to block GOP subpoenas in election probe MORE’s repeated assertions that the 2020 presidential election was rigged against him could hurt Republican efforts to take back the House in 2022.

Luntz noted in an interview on the New York Times podcast “Sway” released Thursday that “more than two-thirds of Republicans believe that the election was stolen,” warning that a widespread and unproven belief that there was rampant fraud last November could turn Republicans off from voting in the midterm elections.

“What Donald Trump is saying is actually telling people it's not worth it to vote. Donald Trump single-handedly may cause people not to vote. And he may be the greatest tool in the Democrats' arsenal to keep control of the House and Senate in 2022,” Luntz said.

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The pollster also said that Trump would be the "odds-on favorite" to win the Republican nomination if he runs again in 2024.

His warning comes as Republicans face an intraparty debate over the future of Rep. Liz CheneyElizabeth (Liz) Lynn CheneyHouse passes sweeping defense policy bill Trump rips Bush for backing Cheney Bush to hold fundraiser for Cheney MORE (Wyo.), the No. 3 House Republican.

Cheney has repeatedly clashed with Trump in recent weeks over his unfounded claims that the November election was “stolen” from him, setting up an expected vote within the House Republican Conference to oust her from her leadership position. 

The favorite to replace Cheney as chair of the conference appears to be Rep. Elise StefanikElise Marie StefanikWyoming county GOP rejects effort to rescind Cheney's party status Stefanik in ad says Democrats want 'permanent election insurrection' GOP leader taking proxy voting fight to Supreme Court MORE (R-N.Y.), a member with a more moderate voting record who morphed into a staunch Trump backer during his 2019 impeachment. 

The dynamic has led to a flood of Democratic criticism that Republicans are shrugging off the facts of the election in favor of currying favor with Trump, and Cheney has vowed she will not stop rebuking the former president over his election fraud claims.

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“History is watching. Our children are watching. We must be brave enough to defend the basic principles that underpin and protect our freedom and our democratic process. I am committed to doing that, no matter what the short-term political consequences might be,” she wrote in a Washington Post op-ed Wednesday afternoon.

House Minority Leader Kevin McCarthyKevin McCarthyFifth House Republican comes out in support of bipartisan infrastructure bill Watch live: McCarthy holds briefing with reporters The Hill's Morning Report - Presented by Alibaba - Biden jumps into frenzied Dem spending talks MORE (R-Calif.), an ardent Trump supporter, earlier this week confirmed he rented a room from Luntz during the coronavirus pandemic, news that was first reported by Fox News host Tucker CarlsonTucker CarlsonCritics blast Tucker Carlson's immigration remarks amid border surge Stefanik in ad says Democrats want 'permanent election insurrection' Joint Chiefs Chairman Milley becomes lightning rod on right MORE.

"Why do Republican officials listen more carefully to Frank Luntz than they do their own voters?" Carlson had asked one night earlier, saying the living arrangement would give Luntz an "outsized influence over the Republican Party's policy positions."

--Updated at 11:43 a.m.