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House and Senate Republicans are in for a chaotic week after disappointing midterms – with GOP leadership elections set for both chambers amid simmering discontent with party bosses.

In the House, Minority Leader Kevin McCarthy, R-Calif., is the only candidate declared for House speaker. However, members of the conservative Freedom Caucus are suspicious of McCarthy and aim to extract procedural concessions from the minority leader that would empower their members.

On the Senate side, some conservative members are calling to delay GOP leadership elections, currently scheduled for Wednesday.

"The Senate GOP leadership vote next week should be postponed," Sen. Marco Rubio, R-Fla., tweeted. "First we need to make sure that those who want to lead us are genuinely committed to fighting for the priorities & values of the working Americans (of every background) who gave us big wins in states like #Florida."

McConnell speaks at presser

Senate Minority Leader Mitch McConnell, R-Ky., aims to be the longest-serving party leader in Senate history. (AP)

Sens. Ted Cruz, R-Texas, Cynthia Lummis, R-Wyo., Josh Hawley, R-Mo., all sent similar tweets Friday. National Republican Senatorial Committee (NRSC) Chair Rick Scott, R-Fla., also called for the elections to be delayed on "Sunday Morning Futures." 

"The leadership in the Republican Senate says, ‘No, you cannot have a plan, we’re just going to run against how bad the Democrats are.' And actually then they cave into the Democrats," Scott said when asked about a letter he is circulating with Sens. Mike Lee, R-Utah, and Ron Johnson, R-Wis., on GOP elections. "Now they want to rush through an election. … They don't want to do any assessment of what we've done wrong."

Even Sen. Lindsey Graham, R-S.C., who has a history as a moderate, joined the calls for a delay Sunday, citing the Herschel Walker race. However, GOP leaders signaled that elections will happen Wednesday as scheduled.

SENATE GOP WON'T MOVE LEADERSHIP ELECTIONS DESPITE CALLS FOR DELAY

"I expect a full and open discussion beginning at Tuesday's policy lunch on our path forward. On Wednesday, we will meet again for our scheduled conference elections," Senate GOP Conference Chair John Barrasso, R-Wyo., wrote in a note to GOP senators, which was obtained by Fox News Digital.

"I welcome the questions and points made in the letter circulated by Senators Rick Scott, Lee and Johnson," Barrasso continued.

Much of the criticism from the right flank of the Senate GOP is for Minority Leader Mitch McConnell, R-Ky. They argue he has taken too many bipartisan votes to hand Democrats wins, and they criticize his support for Ukraine war aid. They are also slamming McConnell for spending millions backing Sen. Lisa Murkowski, R-Alaska, for re-election against a GOP challenger while shunning some Trump-backed candidates in other states.

Kevin McCarthy speaks

House Minority Leader Kevin McCarthy, R-Calif., is the only Republican declared for House speaker. (Reuters/Jonathan Ernst)

However, others are frustrated at Scott himself, who has been at odds with McConnell for much of this year and faced criticism for his handling of NRSC money. Scott has also repeatedly declined to rule out challenging McConnell for Senate GOP leader.

FREEDOM CAUCUS DISCUSSING RIVAL CANDIDATES FOR SPEAKER AMID STANDOFF WITH MCCARTHY OVER HOUSE RULES

"Members are frustrated, and they’re looking for an outlet to have a conversation. There will be a robust discussion at lunch on Tuesday," a Senate GOP aide told Fox News Digital. "There will also be a lot of questions about candidate quality-campaign priorities and mistakes. A lot of these will be directed at Scott, especially if the reports are true that he was preparing to challenge McConnell before Election Day had even concluded."

Both McConnell and McCarthy have support from the vast majority of their members. McConnell has a larger cushion because Senate GOP party elections only require a simple majority of the conference – unlike House speaker elections.

McCarthy, meanwhile, could face opposition from somewhere between 15 and 20 of the caucus' members if he refuses to work with them on their demands for reform, a source familiar with the dynamics in the Freedom Caucus said. Those members are not necessarily opposed to McCarthy, but they want him to make changes to increase their influence before voting for him.

Trump Mar-a-Lago

Former President Trump is expected to announce his 2024 campaign Tuesday. (Phelan M. Ebenhack for The Washington Post via Getty Images)

"There's a point of leverage in these leadership votes," House Freedom Caucus Chairman Scott Perry, R-Pa., said. "We want to have a conversation, devoid of the politics about who is leading, on how the House should operate, how legislation should pass."

With a potential GOP majority likely to be just a few seats, the Freedom Caucus' leverage is significant. If McCarthy does not implement some of their demands, some members are discussing potential replacements for McCarthy, an aide to a Freedom Caucus member said.

Freedom Caucus member Rep. Chip Roy, R-Texas, on Sunday also called to delay House GOP leadership elections until "the final makeup of the U.S. House" is decided.

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There is currently no declared candidate to challenge McCarthy.

The House GOP is also set to hold contentious elections for whip between Reps. Tom Emmer, R-Minn., Jim Banks, R-Ind., and Drew Ferguson, R-Ga., and for conference chair between Reps. Elise Stefanik, R-N.Y., and Byron Donalds, R-Fla. The whip race is especially competitive.

All of this is happening against the backdrop of former President Trump likely announcing his 2024 presidential run Tuesday.

Fox News' Mark Meredith, Kelly Phares, Emily Tubb and Chad Pergram contributed to this report.