The head of the House Freedom Caucus that helped upend last week’s planned choice of a new speaker predicted Sunday members of the rebellious group would “look favorably” on Wisconsin Rep. Paul Ryan for the top job.

Ryan also won praise from more centrist representatives and even from a congressman who has announced his own campaign for speaker. But the 45-year-old chairman of the Ways and Means Committee, who spent the weekend with his family in Janesville, Wis., remained mum on whether he was willing to accept a role he had previously rejected.

The public courting of Ryan spotlighted the search by House Republicans to regain their footing after Majority Leader Kevin McCarthy, R-Calif., unexpectedly withdrew his name from contention at a session that was expected to choose him to succeed Speaker John Boehner, R-Ohio.

Even so, the demands by Tea Party-aligned forces in the House for more decentralized power and more confrontational tactics by GOP leaders were still in evidence.

"If he gets in the race, I think our group would look favorably on him," Rep. Jim Jordan, R-Ohio, chairman of the Freedom Caucus, said on FoxNews Sunday. He called Ryan a "great communicator" and "the kind of messenger our party needs." The caucus, which has about 40 members, officially has endorsed Rep. Daniel Webster, R-Fla., for speaker.

On ABC's This Week, Rep. Jason Chaffetz, R-Utah, who is running for speaker himself, said Ryan "checks every box." Chaffetz called Ryan "a visionary" who "understand the institution."

On CNN's State of the Union, Rep. Tom Cole, R-Okla., an ally of Boehner, said he hoped Ryan would decide to run.

And Rep Mick Mulvaney, R-S.C., a member of the Freedom Caucus, urged Ryan to accept the job. "Sometimes you just need to do it, right?" he said on CBS' Face the Nation. "The country needs you. The party needs you." He said Ryan went "right to the head of the list" of those who could unite warring Republicans.

But in a sign of the challenges involved in the job, Mulvaney also said the deadline to raise the debt ceiling early next month should be used as an opportunity to reduce spending. The deadline to fund the federal government looms in December.

Ryan, who was the GOP nominee for vice president in 2012, has said he wants to focus on the Ways and Means Committee, include a possible overhaul of the tax code, and has expressed concerns about the demands on his family if he were speaker. He has three school-age children.

Meanwhile, Donald Trump, the billionaire businessman who is leading the Republican presidential field, called Ryan “a very nice person” and then speculated about whether his protestations about not wanting the job were real.

"I think he doesn't want it very badly, but you never know," Trump said on Face the Nation. "Maybe he's playing one of the great games of all time. It is speaker of the House — I mean, it's a great position — but he doesn't seem to want it. But I'll bet you that if it was actually offered to him, he would take it."