Congressman Lee Zeldin, who has been mulling a run for chairman of the Republican National Convention for weeks, says he won’t seek the position next year because Chairwoman Ronna McDaniel’s re-election is “pre-baked by design.”

Mr. Zeldin’s announcement comes in the wake of another Republican electoral defeat, in the Georgia U.S. Senate runoff, which is likely to set off yet more Republican infighting.

Mr. Zeldin had been considering seeking the committee leadership in the wake of the historically bad Republican performance in the 2022 midterms. Now, though, he is backing down from that challenge, saying, “I won’t be running for RNC Chair at this time with McDaniel’s reelection pre-baked by design, but that doesn’t mean she should even be running again.”

In his statement, Mr. Zeldin said, “Change is desperately needed,” but claimed Ms. McDaniel’s re-election is already secured, “as if the disappointing results of every election during her tenure, including yesterday in Georgia, do not and should not even matter.”

His statement dismisses challenges by the MyPillow CEO and MAGA loyalist, Mike Lindell, who has announced his candidacy, and a Republican committeewoman, Harmeet Dhillon.

“Republicans are tired of losing and I think that we really need to radically reshape our leadership in order to win,” Ms. Dhillon said in an announcement on Fox News. “And we can’t keep running elections like we did in the ’90s and the 2000s.”

Before other competitors had officially announced, Ms. McDaniel received 101 endorsements, enough to secure re-election in the body of 168 voting members of the committee in the January election.

In his statement, Mr. Zeldin called on Ms. McDaniel to withdraw her candidacy and to listen to the party’s “grassroots,” saying, “Her greatest service to the Republican Party at this time would be to make room for a new Chair.”

“Republican voters already believe that Washington, D.C. is an irredeemable swamp,” he said. “They will be proven right, yet again, if Chairwoman McDaniel moves forward with running for a fourth term, despite her prior pledge not to do so.”

Mr. Zeldin, who has been hearing the complaints of fellow party members since he announced he would consider a run for national leadership, also had some stern warnings for the party itself.

He said the GOP needed to improve in its fundraising, spending, and election integrity efforts, and to recruit better candidates. He also stressed that the party needed to be more of a presence in traditionally Democratic areas of the country.

His announcement comes as the failure of Republicans to deliver in the Georgia runoff ushers in a new season of no holds barred infighting within the party.

In the House, the GOP leader, Representative Kevin McCarthy, is facing a challenge from a representative of the Freedom Caucus, Congressman Andy Biggs, who announced this week he would challenge Mr. McCarthy after weeks of speculation.

“I’m running for Speaker to break the establishment,” Mr. Biggs tweeted Tuesday. “Kevin McCarthy was created by, elevated by, and maintained by the establishment.”

According to an op-ed that Mr. Biggs wrote for the Daily Caller, he sees this as the moment to “dislodge the establishment” and credited President Trump for beginning the movement to do so.

While Mr. McCarthy enjoys more support than Mr. Biggs among Republicans, any fracturing within the party could create a repeat of the 2015 leadership election, when the Freedom Caucus said it would not support Mr. McCarthy even though there was no challenger at the time.

Among Mr. Biggs’s chief demands is a renewal of the motion to vacate the chair, which would allow members of the House to call a vote to remove the speaker of the House from his or her position.

“You have to be able to remove him as speaker if he doesn’t deliver on his promises,” Mr. Biggs said on “The Charlie Kirk Show.”

The motion was last used to attempt to oust Speaker Boehner by Congressman Mark Meadows, a Freedom Caucus member. Although it was not actually brought to a vote, it helped prompt his resignation.

In the Senate, Mr. McConnell is also facing the most opposition to his leadership that he has ever seen, with Senators Braun, Cruz, Graham, Johnson, Lee, Paul, and Rick Scott all voicing their opposition to him publicly.

Mr. McConnell, representing the party establishment, is also in the midst of a battle against Mr. Trump and his influence within the GOP. Most recently, Mr. McConnell commented on Mr. Trump’s calls to suspend rules and laws, including those in the Constitution, until he is made president again or the 2020 election is re-done.

“Anyone seeking the presidency who thinks that the Constitution could somehow be suspended or not followed, it seems to me would have a very hard time being sworn in as president of the United States,” Mr. McConnell told reporters Tuesday.

While it’s not clear who will come out on top, Mr. Trump does lead the field in most 2024 GOP presidential primary polls when his name is included, suggesting he enjoys the support of at least the largest plurality of GOP primary voters.