Washington DC - The race to replace the ousted Republican speaker of the US House of Representatives intensifies this week amid questions over whether anyone is capable of unifying the chaotic party's warring factions.

Kevin McCarthy was ousted in a stunning mutiny last week orchestrated by the far right, leaving efforts to avert a looming government shutdown in a tailspin.

It also raised questions over continuing US military aid to Ukraine and, more immediately, over Congress' ability to respond quickly to a crisis like the violence in Israel and Gaza.

"McCarthy was removed," Representative Matt Gaetz, a leader of the mutiny, told NBC's Meet the Press on Sunday, "because he made multiple contradictory promises to people (in both parties) that ultimately could not be reconciled."

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Bracing for more of the disarray that marked McCarthy's eviction, House Republicans are due to host a "candidate forum" Tuesday to pick their new standard-bearer, followed by a vote behind closed doors Wednesday.

The speaker has to be approved by the full House, however – with both Democrats and Republicans voting – and there is no timeline for a floor vote, leaving the lower chamber in limbo.

"I don't have a lot of advice for my House colleagues, other than this: Follow your heart, but take your brain with you," Republican Senator John Kennedy told NBC News.

And he smilingly advised his tense House colleagues "to be sure to take your meds."

Two declared candidates – McCarthy's longtime deputy Steve Scalise and firebrand Judiciary Committee Chairman Jim Jordan – have been furiously working to lock in support, but a clear frontrunner is yet to emerge.

Jordan's quest to secure the gavel won the coveted endorsement of former president Donald Trump, who has said he is open to a short-term role as caretaker speaker as the race plays out. He plans to visit Capitol Hill on Tuesday, he said.

According to House rules, the speaker does not have to be a member of the chamber, and Trump, who is running for president, has said he would consider taking the gavel for a "30, 60 or 90-day period."

Trump's offer is not seen as a serious possibility, and there has been no broad show of support from Republicans for the ex-reality TV star – who is facing multiple criminal prosecutions – to take the helm, even temporarily.

There would have to be a change in the Republican-drafted rules in any case, as indicted suspected felons are barred from leadership positions.

Trump's endorsement of Jordan appeared to end speculation of his own involvement, although he has not publicly canceled plans for the Washington swing.

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Any hopeful for the office of speaker will need 217 votes, with the House made up of 221 Republicans – and 212 Democrats intent on voting for their own leader, Hakeem Jeffries.

Jordan, a far right populist, told Fox News his priority would be codifying language that says "no money can be used to process or release into this country any new migrants."

Gaetz, for his part, insisted Sunday that the squabble over the speakership would not hinder America's ability to support Israel following the attacks from Gaza.

"There is no ask from Israel that we are unable to meet because it's going to take us a few days to pick a new speaker," he said on NBC.

But with the House paralyzed by the leadership drama and Senate in recess for another week, the November 17 deadline for passing a 2024 budget to avoid the government shutting down is beginning to worry lawmakers.

Many believe Congress will be forced to pass another stopgap funding measure to keep federal agencies open at 2023 spending levels, a repeat of the September 30 compromise that led Republican right-wingers to oust McCarthy.