The National Republican Senatorial Committee chairman, Senator Scott of Florida, said Tuesday he would challenge Senator McConnell’s grip on the caucus during Wednesday’s closed-door Republican leadership vote.

In a letter circulated to his colleagues, Mr. Scott asked for their vote to lead the conference in the upper chamber, saying, “We must start saying what we are for, not just what we are against.”

“I do not believe we can simply continue to say the Democrats are radical,” he wrote. “We need to listen to [voters’] calls for action and start governing in Washington like we campaign back home.”

The vote, which will decide the party’s leader and whip in the upper chamber, is moving forward Wednesday despite calls from some in the party to delay the vote.

A professor of political science at Washington University in St. Louis, Daniel Butler, tells the Sun that Mr. McConnell will almost certainly remain leader because he needs only a majority of his caucus’s support.

“There’s no one in the Senate who has the power to challenge him,” Mr. Butler said. “If someone challenges McConnell, it’s more symbolic because the minority leader doesn’t have many privileges.”

While Mr. Scott’s bid is expected to fall short of the votes needed to win the leadership contest, it does lend a voice to many of the latent grievances among GOP senators that have come to a head since the party’s dismal showing in last week’s election.

Mr. Scott’s letter lists complaints from conference members about the GOP’s lack of a positive message, inability to hold the executive branch accountable, and refusal to debate amendments on the floor.

“Some wonder why we have little coordination with Republican House members,” Mr. Scott wrote. “Some feel pressured to vote for bills that are either against their core beliefs and what they campaigned on or against the best interests of their state.”

According to Mr. Butler, there is another purpose behind this challenge, or any challenge to Mr. McConnell’s leadership: to save face.

“They’re going to do a lot of soul searching and everyone is going to blame someone else because they don’t want egg on their face,” Mr. Butler said.

At least eight Republican senators have called for a delay of the vote until after the Georgia runoff. Senator Cruz warned that a failure to delay the vote would result in “one or more senators” challenging Mr. McConnell.

Outside of the halls of Congress, conservative political activists such as the president of Liberty Consulting, Virginia “Ginni” Thomas, the and wife of Justice Clarence Thomas, have signed an open letter calling to delay elections until after the runoff, as the party considers its position.

“The Republican Party needs leaders who will confidently and skillfully present a persuasive coherent vision of who we are, what we stand for, and what we will do,” they wrote. “There should be no rushed leadership elections.”

Both Mr. Scott’s letter to colleagues and the conservative activists’ open letter suggest that the party needs to better establish the issues on which it stands.

“Why do the Democrats do better than expected? Because for two years they’ve governed as liberals.” Mr. Cruz said on Fox News. “You know what that did? That excited their base. That excited a bunch of young voters that came out in massive numbers, because when you actually stand for something your base gets excited.”

Other lawmakers, like Senator Hawley, have expressed an unwillingness to vote for Mr. McConnell and the status quo, no matter what concessions are offered.

“I’m not going to vote for Senator McConnell. And I’ve been very clear about that and I feel very strongly about that. And I said that before this election,” Mr. Hawley said.

An associate editor at Sabato’s Crystal Ball at the University of Virginia’s Center for Politics, Miles Coleman, suspects that Mr. Scott’s challenge and Mr. Hawley’s support may just be them “carrying [President] Trump’s water.”

“Scott is apparently moving forward with a challenge,” he tells the Sun. “But given the NRSC’s lackluster performance, I’m not sure how much capital he has among his colleagues.”

Messrs. Scott and McConnell have been vying for power in the Republican conference since before the election, attacking each other’s campaign strategy and their support for certain Republican candidates.

Mr. Scott has allied himself loosely with Mr. Trump, arguing that Mr. McConnell did not do enough to support the party’s Senate candidates, especially the likes of venture capitalists Blake Masters and J.D. Vance, or Mehmet Oz, Herschel Walker, and Donald Bolduc. Of that group, only Mr. Vance prevailed in his race.

Mr. McConnell has openly complained about the quality of the candidates who were handpicked by either Mr. Trump or by his allies like Peter Thiel, the tech mogul and Republican donor.

The McConnell-aligned Senate leadership fund often bankrolled these candidates, all of whom were much less successful at fundraising than their Democratic opponents.

This financial burden was compounded by Mr. Trump’s comparatively small campaign contributions and the National Republican Senatorial Committee’s squandering of some $181 million on failed digital fundraising early in the campaign season.

Mr. Butler notes that Mr. McConnell and his allies were largely responsible for picking up the tab for weak candidates.

“I think bad candidates had a big part in it, and I think the Georgia race is a great point to look at,” Mr. Butler said. “There’s no doubt that a Republican could’ve won statewide there because one did.”