Watch for a sequel to the intra-party House fight over the speaker’s gavel to play out again in the upcoming Republican National Committee election.

While most Republicans are celebrating what could ultimately prove to be a pyrrhic victory in the House, their national committee chairwoman, Ronna McDaniel, is facing a similar group of insurgents in her re-election bid later this month.

On Friday, Ms. McDaniel congratulated Speaker McCarthy and the House Republican majority on their election and said they would “bring much-needed accountability to Biden and Democrats in Congress.”

Ms. McDaniel, who was handpicked by President Trump to head the national party after his 2016 election, is now facing her own challenge from the party’s right wing, and many of Mr. McCarthy’s antagonists have thrown their support behind it.

Ms. McDaniel’s challengers in the race to head the RNC are the MyPillow CEO, Mike Lindell, and a Republican committeewoman of California, Harmeet Dhillon, both of whom are criticizing Ms. McDaniel as ineffective.

Since Ms. McDaniel assumed her leadership of the national party, the GOP has performed poorly, losing control of the House in 2018, the Senate and White House in 2020, and delivering a historically bad midterm election in 2022.

These results, alongside the slim House majority and the question of what the party’s relationship to Mr. Trump will be going forward, have divided the party along multiple axes.

Mr. Lindell, widely seen as the less threatening of the two challengers, is a MAGA loyalist and an outspoken supporter of Mr. Trump. However, he openly voiced disappointment in Mr. McCarthy’s election as speaker, even calling out allies for doing so.

“It’s disappointing that anyone went for McCarthy because we need a different input to get a different output,” Mr. Lindell told the Daily Beast. “And that includes Marjorie Taylor Greene.”

Mr. Lindell has garnered some limited support from GOP notables like a failed Senate candidate, Kari Lake, but hasn’t demonstrated enough support yet to mount a serious challenge to Ms. McDaniel.

Ms. Dhillon, on the other hand, has received the public endorsement of at least 18 committee men and women, as well as Representatives Matt Gaetz and Anna Paulina Luna, two prominent opponents of Mr. McCarthy.

Others, such as Representative Byron Donalds, who was himself nominated for speaker, and a conservative pundit, Tucker Carlson, have suggested that they may support Ms. Dhillon even though their statements have fallen short of endorsements.

“Republican voters across the country have not been happy with party leadership across the board, you saw what happened in the Senate, Ronna McDaniel is having a challenge from Harmeet Dhillon,” Mr. Donalds told Fox News. “These leadership challenges are a good thing for our party.”

Although Ms. Dhillon has not gathered enough support to deny Ms. McDaniel a majority, she has chipped away at her support and suggests that more committee men and women might break away from Ms. McDaniel in the time before the election.

Ms. Dhillon is pushing for many of the same objectives as the holdouts in the House speaker’s vote — namely, she wants the party leadership to be held accountable for their electoral failures.

“The party needs to stand for hardcore principles, the party needs to stand for transparency,” Ms. Dhillon said on Glen TV. “Why should any Republican be in favor of a system where you don’t have transparency — accountability when you lose?”

Like the opponents of Mr. McCarthy in the House, both Mr. Lindell and Ms. Dhillon are representing the conservative activist wing of the Republican Party.

Ms. Dhillon says she wants structural changes to the party that would decentralize it and weaken the power of party leadership in Washington. She also is pushing to modernize party fundraising methods, voter outreach efforts, and the party’s legal strategy. She has also put voting reforms at the center of her platform.

In an interview with Just the News, Ms. Dhillon said “we really need to return our party to the party of the Constitution, individual liberties, and small government.”

Mirroring the battle in the House, the challengers in the national committee elections are coming from the party’s right flank rather than the moderate wing, which has united behind Ms. McDaniel.

All of the candidates have close ties to Mr. Trump, with Mr. Lindell being one of his chief evangelists and Ms. Dhillon having served as an attorney defending Mr. Trump against the January 6 committee’s subpoena.

Absent from the race is a candidate representing the faction of the party most eager to move past Mr. Trump, best exemplified by the Senate minority leader, Mitch McConnell, who has said that the party has and will continue to struggle with independents as long as it is perceived as radical.

“We underperformed among independents and moderates because their impression of many of the people in our party and leadership roles is that they are involved in chaos,” Mr. McConnell said following the November election.

Correction: The RNC leadership election takes place later this month. An earlier version contained an incorrect reference to the timing of the election.