With the election for chairman of the Republican National Committee about a month out, candidates hoping to put up any resistance to President Trump’s dominance of the party over the next two years are running out of time.

Congressman John Faso, when asked about sentiment among the party members, told the Sun, “Whoever is elected chairman should not be supporting a particular candidate at this stage.”

Currently, the only candidates to lead the party’s governing body are its current chairwoman, Ronna McDaniel, and the CEO of MyPillow, Mike Lindell, both of whom are historic allies of Mr. Trump.

Ms. McDaniel has already received the endorsement of 101 of the 168 voting committee members, many of whom signed a letter saying her leadership has made the party a “stronger and more effective force for our cause.”

“These are perilous times and the Biden presidency, abetted by the extremist consensus among Democrat Party elites and elected officials, has been, is, and will continue to be a disaster for our nation,” the letter said.

Ms. McDaniel, for her part, has pledged to hold neutral primaries, saying that the national committee will not take sides in a primary and will use the same rules as it did in 2016.

Mr. Lindell has received no endorsements for the position, but did announce his candidacy earlier this week after claiming that a major Republican donor told him that “everybody wants you to be head of the RNC some of them just don’t know it yet.”

“I am 100 percent running for the RNC chairman against Ronna McDaniel,” Mr. Lindell said on Steve Bannon’s War Room. “A hundred percent. I’m all-in Steve.”

The wildcard in the race is Congressman Lee Zeldin, who has been mulling a challenge to Ms. McDaniel’s leadership for weeks, saying there has been an outpouring of support for his leadership.

“Due to the amount of requests I have received from both inside and outside the 168 [committee members] about running to be the next Chair of the Republican National Committee, I am very seriously considering your requests and am grateful for your messages,” Mr. Zeldin said in a letter to Republican National Committee members.

Mr. Zeldin’s claim to the position rests on the midterm performance of Republicans in New York state, which exceeded expectations this year, flipping four congressional seats and helping deliver the Republicans a slim majority in the House.

Although he has not yet formally announced his candidacy, Mr. Zeldin is selling a more positive vision for the party focused on visiting “all communities no matter how blue they are.”

Mr. Zeldin and the organization behind him have received credit for many of the Republican successes in New York. He came closer to winning the governorship than any Republican in recent years, losing to Governor Hochul by about six points.

Regardless of whether Mr. Zeldin decides to run, the party will only have close allies of Mr. Trump to choose from, an issue that could complicate efforts by the party to move beyond the 45th president.

Despite having ties to Mr. Trump in the past, Mr. Zeldin is positioning himself as the reform candidate, telling Fox News that “it is important for the Republican Party with this opportunity to retool — to transform.”

Mr. Zeldin has also publicly questioned whether Ms. McDaniel really has the support of more than 100 members of the committee, suggesting that he’s been led to believe otherwise.

Mr. Zeldin said over the summer that he would be “supportive” of Mr. Trump should he run for president in 2024. He hasn’t elaborated on that position since the election or Mr. Trump’s campaign announcement.

Although none of the potential candidates for chairman of the Republican National Committee have publicly broken with Mr. Trump, Mr. Faso expressed some doubt about the former president’s viability in 2024.

“I would like to see a presidential candidate who can seriously contest New York state and help down-ballot candidates,” Mr. Faso said. “That is surely not Mr. Trump.”