The Republican nominee for speaker of the House, Congressman Jim Jordan, is inching closer to the speaker’s chair after having won key endorsements over the weekend and on Monday. With a razor-thin GOP majority, though, there is no room for error and he could fall short. 

On Monday, Mr. Jordan won the endorsements of some key House GOP leaders who previously said they would not support him on the floor or said they had not made up their minds. The biggest gets for the Judiciary Committee chairman were Congresswoman Ann Wagner — who previously called him a “nonstarter” — and the chairman of the House Armed Services Committee, Congressman Mike Rogers.

After Congressman Steve Scalise withdrew from the race on Thursday, Ms. Wagner emerged from the meeting distraught, telling reporters that Mr. Jordan would be a “nonstarter” due to his lack of vociferous support for Mr. Scalise. By Monday, after two private conversations with Mr. Jordan, Ms. Wagner had been convinced to support him. 

“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,” she said in a statement.  “Jim Jordan is our conference nominee, and I will support his nomination.”

Mr. Rogers had previously floated the idea of working with Democrats to elect a moderate Republican as speaker, and had said he could not support Mr. Jordan given his record. Like Ms. Wagner, he was swayed by the congressman following private conversations. 

“Jim Jordan and I have had two cordial, thoughtful, and productive conversations over the past two days,” Mr. Rogers said on X. “We agreed on the need for Congress to pass a strong NDAA [defense funding], appropriations to fund our government’s vital functions, and other important legislation like the Farm Bill. As a result, I have decided to support Jim Jordan for Speaker of the House on the floor.”

Republicans are set to meet in the basement of the Capitol building on Monday night, where Mr. Jordan hopes to win over his last remaining detractors. Congressman Ken Buck — a fierce conservative and Freedom Caucus member — has taken issue with Mr. Jordan in the past because the Ohio congressman continues to deny that President Biden legitimately won the 2020 election. Congressman Steve Womack told reporters at the Capitol on Monday that Mr. Jordan is too partisan and divisive to lead the conference. 

Mr. Womack, like Mr. Rogers, has also proposed working with Democrats to elect a more moderate Republican speaker. “Nobody in America can get 217 right now out of the Republican conference,” he told CNN on Monday afternoon. “If that becomes apparent to everybody, then at some point in time, we’re gonna have to work across the aisle.”

Several key allies of the now-deposed speaker, Congressman Kevin McCarthy, have refused to say how they will vote on the House floor on Tuesday. Congressman Mario Diaz-Balart and Congressman Don Bacon have refused to commit to any one candidate. 

Congresswoman Victoria Spartz, who supported Mr. Jordan over Mr. Scalise in the nomination fight last week, has withdrawn her support and said she will not vote for him on the floor because he has been making what she calls “behind-the-scenes deals” with other GOP members in order to win their support. She said he may just be “another puppet for the swamp with a better bio.”

One Democrat is bullish on Mr. Jordan’s chances, though. Congressman Jared Moskowitz, a liberal member of Florida, said on X Monday that the Ohio congressman is guaranteed to be the next speaker. 

“Jordan will win the speakership tomorrow,” he said. “It may take multiple rounds. Moderates will cave. This was always the plan by the Freedom Caucus. It wasn’t just about removing McCarthy, but installing one of their own. Freedom Caucus played chess. The rest played checkers.”