A longstanding beef between McCarthy and Scalise has some mainstream Republicans backing hard-right Jordan.

Representative Erin Houchin, a first-term Republican from Indiana, was chosen as the poster child for the new House G.O.P. in the opening months of the 118th Congress, promoted by leaders as a fresh, friendly and broadly appealing face for their party.

Ms. Houchin joined the Main Street Caucus, a group of center-leaning Republicans, and became the president of the freshman G.O.P. class. She was a stalwart ally of former Speaker Kevin McCarthy, voting for the debt limit deal he forged with President Biden, pushing for her Republican colleagues to get behind the stopgap funding measure to keep the government open and generally cheering on the party agenda.

But on Wednesday as Republicans met to select a new speaker to replace Mr. McCarthy, Ms. Houchin was set to deliver a nominating speech for Representative Jim Jordan of Ohio, the right-wing hard-liner who co-founded the ultraconservative House Freedom Caucus.

She is part of a group of lawmakers who view themselves as pragmatic centrists, but who are now lining up behind Mr. Jordan, whose right-wing bent, combative style and close alliance with former President Donald J. Trump have little in common with them.

Representative Kelly Armstrong of North Dakota, another center-leaning Republican, has also publicly backed Mr. Jordan. (Mr. Armstrong serves with Mr. Jordan on the Oversight and Judiciary committees and considers him a close friend.)

Dusty Johnson of South Dakota, the chairman of the Main Street Caucus, and Stephanie Bice of Oklahoma, the vice-chair of the group, have not publicly said who they are backing. But they pushed unsuccessfully for a rule change that would have made it more difficult for Representative Steve Scalise of Louisiana, the No. 2 House Republican who is viewed as the more traditional choice to succeed Mr. McCarthy, to prevail over Mr. Jordan in the race.

They are also close allies of Mr. McCarthy. As members of the Main Street group, their stated purpose is “to develop common sense, pragmatic legislation and promote kitchen-table policies in Congress.” Mr. Jordan was branded by former Republican Speaker John A. Boehner as a “legislative terrorist,” but forged a deal with Mr. McCarthy that moved him from the fringe to the epicenter of politics on the Hill.

The Main Street Caucus, like the conference overall, had members on both sides of the race for speaker, with some aligned with Mr. Jordan and some aligned with Mr. Scalise.

The strange alignment is the ultimate reflection of how much of what happens on Capitol Hill is dictated more by what clique you belong to — and who you or your friends may have a personal beef with — than where you sit on the ideological spectrum.

Mr. McCarthy and his allies have quietly been encouraging members to back Mr. Jordan over Mr. Scalise, with whom Mr. McCarthy has an icy relationship. Mr. McCarthy’s rivalry with Mr. Scalise goes back years and at this point is the stuff of lore on Capitol Hill. At key moments over the past few months, Mr. McCarthy boxed Mr. Scalise out of decision making, describing him to colleagues as ineffective, checked out and reluctant to take positions.

The candidates themselves were both presenting themselves on Wednesday as men who could unite their fractious conference, and move beyond the personal pique that has come to define much of the Republican-on-Republican warfare in the House.

But Mr. Jordan qualified his support for Mr. Scalise, suggesting that he would back the Louisianian only if he won a near-unanimous vote of Republicans — far higher than the simple majority currently required under the party rules. Mr. Jordan’s allies tried to change these rules and raise the threshold, which would make it more difficult for Mr. Scalise to prevail. But the conference voted 135-88 on Wednesday morning to kill the rule change.

“I will support anyone who can get 217 votes,” Mr. Jordan said as he entered the meeting room. “We’ve got to come together as a conference.”