Conservatives are not sold on the idea of Rep. Paul RyanPaul RyanOPINION | Healthcare vote a political death wish for GOP in 2018 The one part of ObamaCare that must be repealed now Senate Dems warn they will block recess appointments MORE (R-Wis.)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 MurrayLive coverage: Senate begins debate on ObamaCare repeal Report: minimum wage bill would benefit 20.7 million workers in 21 states Lawmakers send McCain well wishes after cancer diagnosis 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 AmashOvernight Defense: House passes Russia sanctions deal | McCain returns to Senate | Watchdog opens criminal probe into M camo mistake Overnight Cybersecurity: Senate Judiciary reportedly drops Manafort subpoena | Kushner meets with House Intel | House passes Russia sanctions deal | What to watch at 'hacker summer camp' Overnight Finance: House votes to repeal arbitration rule | Yellen, Cohn on Trump's list for Fed chief | House passes Russia sanctions deal | GOP centrists push back on border wall funding 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 BoehnerBoehner on Trump tweets: He gets 'into a pissing match with a skunk' every day Boehner predicts GOP will 'never' repeal, replace ObamaCare Sudan sanctions spur intense lobbying 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 BoehnerBoehner on Trump tweets: He gets 'into a pissing match with a skunk' every day Boehner predicts GOP will 'never' repeal, replace ObamaCare Sudan sanctions spur intense lobbying 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.