As many Republicans urge Rep. Paul Ryan (R-Wis.) to make a bid for House speaker, some hardline conservatives say he's been too willing to compromise -- the same complaint that plagued departing Speaker John Boehner (R-Ohio).
But Rep. Jim Jordan (R-Ohio), chairman of the conservative Freedom Caucus, said Sunday that members would "look favorably" on Ryan for speaker, so long as he agrees to their demands for policy changes within the GOP conference.
"I think he'd be a great messenger," Jordan said on "Fox News Sunday." "He'll come in front of our group and talk to us -- I think our group would be favorable towards him, but we're not there yet."
The House GOP is scrambling to find a new speaker after Majority Leader Kevin McCarthy (R-Calif.) dropped out of the running on Thursday moments before the conference was set to vote.
The Freedom Caucus endorsed Rep. Daniel Webster (R-Fla.), whom Jordan said they still support because of his commitment to change procedures for things like committee assignments, bringing bills to the floor and making amendments.
Freedom Caucus members say the group's qualms with Boehner and others within the GOP are largely about process and making sure members are heard. But they also have more ideological aims, such as impeaching IRS Commissioner John Koskinen and changing entitlements.
Jordan said he thinks Ryan would have to commit to the rule changes they're seeing.
"I think he will agree to that," Jordan said. "I think the next speaker has to agree to that because this place has got to change. ... We need a shake-up, and this is exactly what the people are demanding."
Rep. Raul Labrador (R-Idaho), a member of the Freedom Caucus, said Sunday on CNN's "State of the Union" that they won't drop support for Webster for an undeclared candidate, referring to Ryan, who he said is a good friend.
There are other options as well, he said, such as Rep. Rob Bishop (R-Utah). Labrador also noted that another speaker candidate, Rep. Jason Chaffetz (R-Utah), is closer to the Freedom Caucus ideologically.
"We want to make sure we're together as a conference," Labrador said. "We should be fighting the Democrats, not the Republicans."
Rep. Tom Cole (R-Okla.), appearing with Labrador on CNN, insisted their differences are more about tactics than ideology.
"I think a lot of things are being aired that probably needed to be aired," he said.
The Boehner ally said he hopes Ryan will run.
"I just have enormous confidence it's the right man at the right moment," Cole said. "But again, whether or not he chooses to do that is up to him."
Even though he's a candidate, Chaffetz said on ABC's "This Week" that he, too, hopes Ryan will run.
Still, Chaffetz said he thinks he's capable of the job, although "there are other people that are better qualified" than he is.
"But I do think I bridge that gap, and that's the case that I'm making," Chaffetz said. "If there's somebody better who can unite us, I'll support them. But you know you're either part of the solution or part of the problem. I've -- right or wrong -- thrown myself in there and said, 'I think I can do this.'"