Conservatives are not sold on the idea of Rep. Paul RyanPaul RyanPoll: Trump voters have positive opinion of president Overnight Regulation: Senators call for 'cost-effective' regs | FCC chief unveils plans to roll back net neutrality Overnight Tech: FCC chief unveils plan for net neutrality rollback | Tech on Trump's sweeping tax plan | Cruz looks to boost space industry 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 MurrayPatty MurrayTrump said he would create ‘more jobs and better wages’ — he can start with federal contractors Sanders, Dems introduce minimum wage bill Week ahead: Senate panel to vote on Trump's FDA pick 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 FlemingCoast Guard suspends search for missing Ohio plane Freedom Caucus member to bring up bill on impeaching IRS chief GOP seeks to make it 52 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 AmashThe Hill's Whip List: Who to watch on GOP's new ObamaCare bill Oversight Dems want vote on Trump tax return bill Greens take climate fight to GOP town halls 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 BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection 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 BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection 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.