An intense leadership fight inside the Republican National Committee is pitting a three-term incumbent with a losing record against a combative challenger, a sign of the party’s struggle to regroup after November’s disappointing midterm elections.

Ronna McDaniel, who has led the RNC since shortly after being selected in late 2016 by Donald Trump when he was president-elect, is favored to win a fourth two-year term as chair at a Jan. 25-27 meeting in Southern California, some veteran committee members said.

Harmeet Dhillon, an election lawyer from California who has represented Mr. Trump in court and been on the RNC for six years, is her main competitor. MyPillow Inc. Chief Executive Mike Lindell has also thrown his name into the mix, although it would be unusual for the national party to select a leader who isn’t already an RNC member.

Harmeet Dhillon has run an aggressive campaign that some members say has fueled division in the RNC.

Photo: JIM URQUHART/REUTERS

The RNC raises hundreds of millions of dollars each election cycle for campaigns nationwide, works to turn out voters and oversees presidential primary debates and national conventions. The contest for its new leader has focused less on substantive differences in how each candidate would lead the party and more on whether Ms. McDaniel is to blame for three election cycles of disappointing results.

During Ms. McDaniel’s tenure, the GOP lost the House in 2018, followed by the White House and Senate in 2020. The party won a narrow majority in the House in November, but failed to secure Senate control and underperformed historic norms in an economic environment that should have been favorable to the party not controlling the White House.

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The RNC race is playing out as the GOP braces for a presidential primary campaign between Mr. Trump and potential Republican candidates who have suggested that the party needs a new face and fresh strategies to win more independent voters and elections.

Mr. Trump has so far remained neutral in the first contested RNC leadership election in 12 years, although some of his supporters have helped mobilize opposition to Ms. McDaniel. Some of the 168 voting members in the normally clubby RNC say they don’t need any convincing to make a change.

“If a coach has multiple losing seasons, there is a change made,” said Beth Campbell, an RNC member from Tennessee who plans to vote for Ms. Dhillon.

Ms. Dhillon, 54 years old, has run an aggressive campaign that some members said has fueled division in the RNC. She has faulted the “consultant class” for giving the committee and some of its candidates bad advice, and is touting her experience with election law and skills as a communicator. “I see a lack of strategy and a lack of leadership,” she said in an interview.

Ms. McDaniel, in an interview, pointed to turnout gains and other accomplishments under her leadership and said Ms. Dhillon is using disinformation to attack her tenure unfairly.

Then-President Donald Trump and RNC Chair Ronna McDaniel at a rally in Missouri four years ago.

Photo: Jeff Roberson/Associated Press

“The biggest problem in our party right now is infighting, the circular firing squad,” Ms. McDaniel said. “If you look at Arizona, for example, there is more rancor within the Republican Party than I’ve ever seen.”

The leadership of the Republican Party of Arizona in December called on Ms. McDaniel to resign her post. Stark disagreement over Mr. Trump’s false claims that he won the 2020 election have torn the state GOP apart, and the party lost a Senate race and governor’s race there in November.

Several other state party committees in recent weeks have passed no-confidence votes against her. On Friday, the Republican Party of Florida is scheduled to consider that question.

“She has lost the trust and the respect of the average Republican,” said Anthony Sabatini, GOP chair in Florida’s Lake County and the leader of the drive in the state against Ms. McDaniel. “They don’t think she’s a good tactician or has done a good job.”

Some prominent GOP donors, including Home Depot Inc. co-founder

Bernie Marcus, are calling for a leadership change at the RNC. In a letter of support last week for Ms. Dhillon, a group of 27 donors that didn’t include Mr. Marcus said the party’s losses demand a change. The donors said consultants had plundered party resources.

“The once great party of Lincoln is on the verge of permanent irrelevance if we fail to come together to correct course,” the letter said.

In response, Ms. McDaniel said she is constantly reviewing the effectiveness of consultants and has put in place an extensive bidding process for vendors. She pointed to her own endorsements from some key donors, including Elizabeth Uihlein, the billionaire co-founder of the privately held Uline office-supply business.

Ms. McDaniel, before her most recent selection as chair in 2021, had indicated that she didn’t plan to run for another term in 2023. But less than a week after November’s election, she said she would again seek the post.

Ms. McDaniel said she opted to run again because she thinks she can more quickly help the party prepare for a fast-approaching presidential campaign than a new person could. She also said she is being unfairly blamed for the party’s 2022 election shortcomings because she and her committee don’t pick candidates.

“I think there is intentional disinformation about what the RNC does,” she said. “I keep hearing this coach analogy. If you are the coach, you get to pick the players.”

Ms. McDaniel, the 49-year-old niece of Sen. Mitt Romney (R., Utah), defended her stewardship of party resources and pushed back against Ms. Dhillon’s suggestions that the committee has spent too much on private jet flights, which the incumbent said is sometimes needed because of security surrounding such people as Mr. Trump when they are taken to party fundraising events.

“These are also intentionally dishonest and misleading attacks, unfortunately, hurting the RNC, being pushed by a member of the RNC,” Ms. McDaniel said, adding that she has flown on commercial flights 320 times in the past two years.

Among her accomplishments, Ms. McDaniel points to opening 38 community centers in 19 states to help make inroads with Hispanic, Asian and Black voters, and recruiting tens of thousands of poll workers and watchers. The RNC filed more than 80 lawsuits during her tenure that she says were designed to protect election transparency and integrity.

Bill Palatucci, a longtime RNC member from New Jersey, said unseating an incumbent RNC chair isn’t easy because there are many tools at their disposal to curry favor, including assignments on popular subcommittees and how much funding is delivered to state parties.

While he expects Ms. McDaniel will win, Mr. Palatucci said, “It’s never over until it’s over.”

Bruce Hough, a longtime RNC member from Utah who plans to support the current chair, said the party’s losses were more attributable to Mr. Trump than to Ms. McDaniel. “These were candidates who won primaries, but could not win general elections,” he said.

A person close to Ms. McDaniel said she has received death threats and personal attacks on social media as part of her re-election bid.

Ms. Dhillon said she makes no apologies to RNC members who have been inundated with emails from grass-roots Republicans trying to influence their vote. “Ronna won’t leave, she’s defending a failed record, and my only way of running against her is to point out those failures and say what I would do differently,” she said.

Write to John McCormick at mccormick.john@wsj.com