WASHINGTON — Republican hardliners on Sunday said they could support Rep. Paul Ryan for House speaker, opening a potential bridge between bitterly divided Republican factions.

Ryan’s willingness to try to steer a caucus that some say can’t be led is a big “if.” The Ways and Means chairman and 2012 vice presidential candidate is a father to young children and has said publicly he does not want the job. Ryan is home in Wisconsin consulting with his family, away from colleagues, including retiring House Speaker John Boehner, who are pressuring him to run.

But on Sunday, members of the rebel Freedom Caucus and the Republican establishment broadcast their potential support for Ryan, creating what appears to be the sole point of agreement between them after a tumultuous week that left the race for speaker wide open. There are other candidates for the job that’s second-in-line to the presidency, but the path forward for now seems to rest on Ryan’s answer.

“Paul Ryan is a good man. He’s a great communicator, the kind of messenger I think our party needs. And certainly, if he gets in the race, I think our group would look favorably on him,” Freedom Caucus Chairman Jim Jordan, R-Ohio, said on “Fox News Sunday.”

The prospect of Ryan as speaker arose after a rollicking two weeks on Capitol Hill, in which Boehner announced his resignation and his heir apparent, Majority Leader Kevin McCarthy, abruptly withdrew his candidacy. Freedom Caucus members had presented McCarthy with a list of demands he and top aides concluded could be next to impossible to meet, including a seat at the leadership table, a role in selecting committee chairs and members and more votes on their legislative proposals.

A leadership vacuum resulted, with Ryan the only person widely deemed to fill it. He has said repeatedly he doesn’t want the job.

Rep. Raul Labrador of Idaho agreed that it’s possible that he and other members of the House Freedom Caucus would swing behind Ryan, or others. But first, Labrador said, any candidate needs to talk to the caucus and address the concern that the speaker should more effectively push the Republicans’ agenda before making deals.

“It’s not about the who, it’s about the what,” Labrador told CNN’s “State of the Union” on Sunday. “What are we going to do in the House to change the culture? What are we going to do so we can get 247 Republicans together on the same page? What are we going to do so that every member of the conference feels they’re actually valuable and that they are doing the things they need to do?”

Even Rep. Jason Chaffetz, R-Utah, who launched a bid for speaker late last week, said he could be open to the prospect of Ryan as speaker.

“I think he checks every box. He’s got the great experience, he’s a visionary, he understands the institution, he’s a great spokesperson,” Chaffetz said.

Chaffetz, the chairman of the House Oversight and Government Reform Committee, said on ABC’s “This Week” that the next speaker should change the way legislation and negotiation are done.

“We allow these good bills and ideas to percolate from the bottom up, rather than the top down-driven process where the speaker is telling the body what to do. I think the speaker works for the conference, the House Republicans,” he said.

A member of Republican establishment allied with Boehner also expressed support for Ryan.

“I just have enormous confidence it’s the right man at the right moment,” Rep. Tom Cole of Oklahoma said on CNN’s “State of the Union.”

Cole also tried to downplay the differences between factions, and appealed for calm.

“Our disagreements tend to be tactical, not theological. We actually believe in the same thing,” Cole said, voicing confidence that the dispute will eventually be worked out. “It’s not like we’re going to be without a speaker.”