If Republican heads are going to roll because of last week’s election results, they probably won’t be at the Republican National Committee.

Despite presiding over one of the more disappointing elections in decades for the Republicans, the head of the committee, Ronna McDaniel, is signaling that she is not about to step aside when the party meets in January to select a new leader.

According to Politico, Ms. McDaniel told committee members on a call Monday that she would run again for the post if its members want her to, and several chimed in to say they did. Ms. McDaniel needs the support of a majority of the 168-member body in order to keep the office, and as many as 100 have reportedly pledged that support.

Last week’s lackluster performance has led some members of her party to call for new leadership. Ms. McDaniel was selected to head the committee by President Trump after he won the 2016 election, and would remain in the post through the 2024 presidential campaign if she is re-elected.

A number of potential challengers have surfaced in the days since last week’s election, among them Congressman Lee Zeldin, who nearly defeated an incumbent Democratic governor in deep blue New York last week; Governor Noem of South Dakota; and a former Trump administration official, Mercedes Schlapp.

Another potential challenger, current co-chairman Tommy Hicks, a longtime friend of Mr. Trump’s, said in a letter circulated to party members Monday that he would not be seeking another term. “My family and I decided that I would take a step back from politics and return focus to my business,” Mr. Hicks said.

All of the names being bandied about as potential new leaders have one thing in common — they are all, publicly at least, loyal to the man who many are blaming for the Republicans’ poor showing. The chorus of Republicans calling Mr. Trump politically toxic in the wake of last week’s vote does not appear to be getting through to anyone at the national committee.

Confounding the discussion is Ms. McDaniel’s pledge that the party remain “neutral” during the primary process, a commitment that has been enshrined in the committee’s bylaws.

Even if new leadership did come forward to express an interest in moving on from Mr. Trump, the committee could have a hard time exorcising the former president from the political process. Mr. Trump is widely expected to announce Tuesday that he will seek the Republican nomination again in 2024, and there may not be much the party can do to stop him.

Mr. Trump is the party’s main moneymaker and his headshots still appear on the vast majority of the party’s fundraising pleas to small donors. As long as he has the signatures required to get on the various state primary ballots, there is little the party could do to thwart him. The days when party bosses gathered in the proverbial smoke-filled rooms at national conventions to select candidates have been over since the early 1970s.

Correction: Noem is the spelling of the last name of the South Dakota governor. The name was misspelled in an earlier version.