Which means that, unless Jordan can overcome his skeptics and push to victory on the floor in the next several days, the only way forward might be with Democrats. A group of centrist Democrats wrote to Acting Speaker Patrick McHenry (R-N.C.) on Friday to propose a limited agenda and some perks for the opposing party in exchange for temporarily restarting House business during a time of global crisis.

Some self-described GOP pragmatists have suggested that if Republicans can’t chart a course on their own, they could cut a deal with Democrats to break the 10-day impasse.

“At some point we have to do a bipartisan deal. I mean, they don’t want to acknowledge it, but these guys do not want to govern,” Rep. Don Bacon (R-Neb.) said of his own party’s conservatives.

But as desperation creeps into the GOP while Jordan pushes to lock down the gavel, it’s clear that any attempt to further empower a caretaker speaker would fall short within their own party. McHenry has indicated that his future role as acting speaker is up to his colleagues to settle — even as the Nov. 17 shutdown deadline draws closer and Israel seeks U.S. aid — but his fellow Republicans simply can’t agree on anything.

Rep. Max Miller (R-Ohio) stood up in a closed-door GOP meeting on Thursday to propose empowering a fill-in speaker for 90 days in a bid to prevent weeks of further havoc in the chamber. Miller, one of two Jewish Republicans in Congress, suggested allowing the House to resume business, according to two people granted anonymity to recount the private discussions.

Inside the room, however, the idea ran into a wall of resistance. As Rep. Rich McCormick (R-Ga.) later described the scene: “It wasn’t well received. That’s not what the conference wants.”

Despite that, the push is unlikely to die anytime soon. After a tumultuous 36 hours that toppled heir apparent Scalise, the Republicans’ best hope for a speaker — at least, currently — is now ultraconservative Jordan, who is still short of the 217 votes needed. Behind the scenes, that historic impasse is sparking ongoing conversations about a hold-over speaker with powers to prevent at least a total paralysis of the floor.

“The world is on fire, and we need to address things. We can’t continue down this way,” said Rep. David Joyce (R-Ohio), leader of the Republican Governance Coalition and one of those pushing to empower McHenry.

Joyce began circulating a resolution on Thursday night that would do just that — clarifying and expanding the powers of a position that was created post-Sept. 11 without a clear picture of the actual duties. He’s even raised the idea with top Rules Committee Democrat Rep. Jim McGovern of Massachusetts.

“If you have a speaker, the speaker should have power,” Joyce said.

He’s not alone. A group of McCarthy allies, including Rep. Garret Graves (R-La.), have held loose discussions with other members all week, as have institutionalists like Reps. Tom Cole (R-Okla.). There’s also growing interest among exasperated centrists from swing seats, such as those in the New York delegation.

Rep. Nick LaLota (R-N.Y.) acknowledged that McHenry has been able to do little more than open the floor, but said: “That may change next week if we don’t have a bonafide speaker.”

Not everyone agrees. Any maneuver to empower McHenry would face plenty of resistance from conservatives, many of whom see the Financial Services chair as little more than an extension of McCarthy. One Freedom Caucus member privately remarked that if McHenry is given more sway, “Kevin is ultimately going to be running the show.”

Rep. Anna Paulina Luna (R-Fla.) put it this way about McHenry: “Really cool guy … terrible negotiator.”

It’s also an idea that many corners of the Democratic Party won’t like.

Former Speaker Rep. Nancy Pelosi (D-Calif.), for one, was clear that it is the GOP’s “responsibility” to elect their own speaker before reopening the House floor, adding: “It’s up to them. It’s up to them to get their act together.”

There’s another problem: McHenry himself isn’t on board with the plan, according to multiple lawmakers. (Joyce characterized the North Carolina Republican as “unhappy” with him for pushing it.)

Instead, McHenry is privately telling Republicans that he believes he is in a temporary role meant to guide the conference to a new leader, joking that he is speaker number “55.5” — acting only as the bridge between McCarthy and his successor.

Then there’s the fact that not everyone in the House GOP even agrees the floor needs to be reopened.

Freedom Caucus Chair Rep. Scott Perry (R-Pa.), who’s supporting Jordan, even questioned whether the House needed a speaker vote.

“As the Constitution was written, we can go without a speaker for a long time because Congress actually doesn’t have to be in,” Perry said, adding that he opposes empowering McHenry temporarily.

Even so, it’s not just the GOP’s more centrist-leaning members who are concerned by the paralysis. Even Rep. Andy Biggs (R-Ariz.), while not sold on empowering McHenry, said he already had conversations with the parliamentarian before former McCarthy’s ouster about what powers a temporary speaker has under the current rules.

Underscoring some of the uneasiness about giving an unelected speaker too much power, Biggs added that if Republicans move to formally boost McHenry’s authority, it needed to be narrow and temporary.

“There is one interpretation that would allow [McHenry] to bring stuff to the floor” without a rules change, Biggs said. But he added that if there was one, “it would have to be very specific” and have a deadline.

Rep. Thomas Massie (R-Ky.) disagreed. As the House neared 10 days without a speaker, he argued that Jordan has outside support that Scalise lacked and could pressure centrist holdouts to back him on the floor.

“I think it’s premature to give up on electing a speaker. I think we had two candidates and one dropped out. Let’s put the other one on the floor,” Massie said. Even so, he predicted “multiple rounds” of voting on the floor — just like in January.

If that doesn’t work, centrists like Bacon have another idea, too. The Nebraskan floated a longer-term deal with Democrats that involves changes to certain House rules, such as requiring bipartisan support for boosting the number of members it takes to oust a speaker.

“There’s got to be some sort of compromise made to get to 218,” he said. “Because these guys, you have eight to 10 of them are never happy. It’s going to be 100 percent for them or zero.”

Nicholas Wu contributed.