Representative Jim Jordan of Ohio picked up steam on Monday in his bid to become speaker, winning over several of his biggest opponents in the fractured G.O.P. ranks even as deep reservations remained about elevating him to the top post in the House.
Several mainstream Republicans who had said they could not countenance a vote for Mr. Jordan, the hard-line co-founder of the ultraconservative House Freedom Caucus, fell into line after a pressure campaign by his right-wing allies and a series of one-on-one calls with him.
Their reversals suggested that Mr. Jordan was within striking distance of the 217 votes he would need to be elected in a planned vote around noon on Tuesday. But the outcome remained far from certain.
“The role of the speaker is to bring all Republicans together. That’s what I intend to do,” Mr. Jordan said in a letter sent to his Republican colleagues on Monday. In it, Mr. Jordan acknowledged the deep divisions in the G.O.P. and said he would give more lawmakers input into the party’s agenda.
“We will make sure there are more Republican voices involved in our major decisions beyond the Five Families,” he wrote, using House G.O.P. lawmakers’ shorthand for the various factions in their ranks. It is also a reference to warring Mafia families.
People close to Mr. Jordan, the chairman of the Judiciary Committee, said the number of Republican holdouts had shrunk from around 50 to around 10. That is still enough to block his election, but he planned to press ahead anyway, counting on his remaining opposition to cave under pressure on the House floor.
Leaving a two-hour meeting of House Republicans on Monday night at the Capitol, Mr. Jordan indicated he would force a series of floor votes on Tuesday until Republicans had chosen a speaker.
“We need to get a speaker tomorrow,” he said. “The American people deserve to have their Congress, their House of Representatives working. And you can’t have that happen without a speaker, so we need to do that. Plus, we need to be helping our best friend and closest ally, Israel.”
Should Mr. Jordan, 59, become speaker, it would cap an extraordinary rise in Congress that propelled him from a right-wing rebel on the fringes of his party to the post that is second in line to the presidency.
His ascent would be the clearest indicator yet of how far House Republicans have moved to the right during Mr. Jordan’s 16 years in the chamber. It would also show how strong a grip former President Donald J. Trump, who counts Mr. Jordan among his closest allies, has on the party.
A small band of hard-right Republicans, most of whom are supporters of Mr. Jordan, forced Kevin McCarthy out as speaker two weeks ago. Then a broader group of Mr. Jordan’s supporters refused to back the party’s initial chosen successor for the post, Representative Steve Scalise of Louisiana, who abruptly withdrew last week.
The downfalls of Mr. McCarthy and Mr. Scalise left many mainstream Republicans bitter that the will of a majority in their ranks had not been honored. Several argued that elevating Mr. Jordan would reward “bad behavior.”
In his conversations with holdouts, Mr. Jordan said he listened to “frustrations about the treatment of Kevin McCarthy and Steve Scalise and the events of the past month.”
Several members spoke against Mr. Jordan’s candidacy during the closed-door meeting on Monday night in the basement of the Capitol.
One, Representative Mike Kelly of Pennsylvania, proposed giving Representative Patrick T. McHenry of North Carolina — the temporary speaker whose role is primarily to hold an election for a speaker — more power to carry out the chamber’s work for the next month until the conflict could be resolved.
“When you go outside the rules of your own conference because you didn’t get your way, I think that is truly sad,” Mr. Kelly said, using a profanity to describe the tactics Mr. Jordan’s supporters used to undermine Mr. Scalise’s victory. “That is a real indictment of who you are.”
Mr. Jordan won the party’s nomination after Mr. Scalise’s withdrawal, but scores of Republicans signaled that they would not support him on the House floor.
That was before Mr. Jordan and his allies went to work with a public pressure campaign against lawmakers who were resisting his election.
Amy Kremer, a political activist who also leads Women for America First, which organized a “Stop the Steal” rally on Jan. 6, 2021, posted a hit list of 12 members on Friday. She listed their office phone numbers and urged her followers to call them and tell them to support Mr. Jordan. The list included Representatives Ann Wagner of Missouri, Mike Rogers of Alabama and Carlos Gimenez of Florida, all of whom had publicly stated their opposition to Mr. Jordan.
By Monday morning, two of the three had declared their support for him.
Ms. Wagner, a supporter of Mr. Scalise, had called Mr. Jordan’s candidacy a “nonstarter” and accused him of behaving classlessly after his loss to Mr. Scalise. But on Monday, she said Mr. Jordan had won her over.
“Throughout my time in Congress, I have always been a team player and supported our Republican nominees out of conference,” Ms. Wagner said in a statement. “Jim Jordan and I spoke at length again this morning, and he has allayed my concerns about keeping the government open with conservative funding, the need for strong border security, our need for consistent international support in times of war and unrest, as well as the need for stronger protections against the scourge of human trafficking and child exploitation.”
Mr. Rogers, the chairman of the Armed Services Committee, said he had “two cordial, thoughtful and productive conversations” with Mr. Jordan, and received assurances about carrying out the functioning of government and funding of the military.
Mr. Jordan also picked up support from Representative Ken Calvert of California, the chairman of the Defense Appropriations Subcommittee, who said he had spoken with Mr. Jordan “about how we must get the House back on a path to achieve our national security and appropriations goals.”
Another initial holdout, Representative Vern Buchanan of Florida, said he remained “deeply frustrated” but would vote for Mr. Jordan based on the need to have a functioning House.
“I believe the future and immediate well-being and security of our country is too important and the need for Republicans to move forward united is greater than ever,” Mr. Buchanan said.
Still, there were some members of Congress who were unmoved.
Mr. Gimenez said he would continue to support Mr. McCarthy and refuse to give in to the hard-right rebels who had ousted him.
“Last week, eight colleagues joined all the socialist Democrats to carry-out a coup against our duly-elected Republican Speaker Kevin McCarthy,” Mr. Gimenez wrote on the social media site X. “These 8 lit the fuse & every Democrat in Congress provided the gunpowder to overthrow the will of 96% of Republicans in Congress who voted to retain Speaker McCarthy. I will not partake in this despicable coup. Speaker McCarthy should have never been removed to begin with.”
Kayla Guo and Robert Jimison contributed reporting.