Conservatives are not sold on the idea of Rep. Paul RyanPaul Davis RyanWary GOP eyes Meadows shift from brick-thrower to dealmaker Budowsky: Why I back Kennedy, praise Markey Democratic super PAC quotes Reagan in anti-Trump ad set to air on Fox News: 'Are you better off?' MORE (R-Wis.) as Speaker.

While top House Republicans are trying to push a reluctant Ryan into the job, on the grounds that he alone can unify the conference, conservative lawmakers gave a decidedly cool response Friday when asked if they want him to be their new leader.

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Several GOP lawmakers noted that Ryan has repeatedly said he is not interested in the job, while appearing less than convinced that he is the only viable candidate.

“The name came out,” said Rep. Tim Huelskamp (R-Kan.) after Friday’s private GOP meeting. “Last I knew, [Ryan] definitely didn’t want to do it.”

Huelskamp also criticized one of Ryan’s major legislative achievements in Congress, the two-year budget agreement he hammered out with Sen. Patty MurrayPatricia (Patty) Lynn MurrayPelosi huddles with chairmen on surprise billing but deal elusive House approves two child care bills aimed at pandemic GOP, Democratic relief packages B apart on vaccine funding MORE (D-Wash.) in 2013.

The Kansas Republican noted that he opposed the pact, “as did a lot of other people,” and pointed out lawmakers in both parties are now pushing to further ease the spending caps it established.

“A lot of folks want to break that up already,” Huelskamp said.

House Freedom Caucus Chairman Jim Jordan (R-Ohio) declined to weigh in on Ryan as Speaker, noting only that his group had earlier backed Rep. Daniel Webster (R-Fla.) for the job.

And Rep. John FlemingJohn Calvin FlemingTrump wants Congress to delay Census deadlines amid pandemic Meadows sets up coronavirus hotline for members of Congress The Hill's Morning Report - Iran strikes US bases in Iraq; Trump to speak today MORE (R-La.) dismissed the idea of a Ryan groundswell.

“I think that’s more media-driven. I think that’s you guys who keep talking about Paul Ryan,” he said. “Paul has made it clear he’s not interested."

For his part, Ryan has repeatedly rebuffed calls for him to take over as the head House Republican. On Friday, a Ryan spokesman reiterated that the 2012 vice presidential candidate is “still not running for Speaker.”

Rep. Justin AmashJustin AmashPeter Meijer wins GOP primary in Amash's Michigan district Amash confirms he won't seek reelection Democrats fear US already lost COVID-19 battle MORE (R-Mich.) said the Freedom Caucus continues to back Webster. Still, he said Ryan would probably be a more palatable option compared to BoehnerJohn Andrew BoehnerWary GOP eyes Meadows shift from brick-thrower to dealmaker Bottom line Cheney battle raises questions about House GOP's future MORE or House Majority Leader Kevin McCarthy (R-Calif.), who dropped out of the Speaker’s race on Thursday.

"I think that Paul Ryan would be a more acceptable candidate than the current leadership team, primarily because he’s not in the current leadership team. And I believe he’d provide a different approach," Amash said.

Rep. Pete King (R-N.Y.) said that if hardliners reject Ryan, "they would lose all credibility."

"Listen, these guys don't know what they're doing anyway. They would prove to the American people they have no idea what they're talking about," King said.

The level of support for Ryan among conservatives is critical, given that it was rightward pressure that originally pushed out Speaker John BoehnerJohn Andrew BoehnerWary GOP eyes Meadows shift from brick-thrower to dealmaker Bottom line Cheney battle raises questions about House GOP's future MORE (R-Ohio) and helped upend the campaign by McCarthy to replace him.

Despite being broadly popular among House Republicans, McCarthy stunned his colleagues Thursday by dropping out of the race, minutes before a vote he was expected to win.

He told members he was removing himself because he did not think he would be able to unite the divided Republican conference and win over enough conservatives.

—Sarah Ferris and Cristina Marcos contributed.