U.S. Senate Republicans meet for leadership elections at the U.S. Capitol in Washington
U.S. Senator Mike Braun (R-IN) arrives as Senate Republicans meet for leadership elections at the U.S. Capitol in Washington, U.S., November 16, 2022. Reuters

Some of Donald Trump's closest allies in the U.S. Congress stepped up their attacks on their Republican leaders on Wednesday, as the former president's party struggled to come to terms with its weaker-than-expected election performance.

In the U.S. Senate, a group of staunch Trump allies led by Senator Rick Scott mounted the first challenge against Senate Republican leader Mitch McConnell in his 15-year reign as party chief, contending that the "D.C. swamp" was to blame for the party's inability to win a Senate majority.

Trump has repeatedly called for McConnell's ouster, and has promoted Scott as a replacement, since McConnell recognized Democrat Joe Biden as the winner of the 2020 presidential election. Trump, who launched his own 2024 White House candidacy on Tuesday, falsely claims he lost because of fraud.

Republican Senator Mike Braun, a conservative who backed Scott, criticized McConnell's decision not to put forward an agenda for voters during the midterm campaign.

"The Democrats outmaneuver us in every election," Braun said as Republicans met to choose their leaders for the next two years.

"And, you know, we're political wallflowers," he added. "We don't have an agenda. We don't have a business plan. That doesn't work anywhere else."

But other Republicans have said it is time for the party to move on from Trump, after many of his endorsed candidates for the Senate and House of Representatives lost races in an election that left the Senate in the hands of Democrats and Republicans with hopes of little more than a narrow House majority.

"President Trump has lost three (elections) in a row. And if we want to start winning, we need a new leader," Senator Mitt Romney told reporters.

In the House, conservative Republicans continued to bash party leader Kevin McCarthy, a day after he overcame a challenger for the chamber's top job of House speaker.

"Minority Leader McCarthy still doesn't have the votes to become the next House speaker. Yesterday's vote shows there is increasing frustration with the status quo," Representative Andy Biggs, who challenged the California Republican but lost in a 188-31 vote, wrote on Twitter on Wednesday.

"The American people want us to turn a page," Biggs said.

While Senate Republicans met in the morning to vote for party leaders, House Republicans were due later in the day to consider chamber rules for the next Congress, assuming they succeed in capturing the House.

Republicans were just one seat away from securing a House majority on Wednesday, with the final outcome hanging on tight races in states such as California.

The hard-line conservative House Freedom Caucus, whose members include Biggs, is pushing for rules changes that would, among other things, make it easier for members to oust a speaker.