Kevin McCarthy
Republicans have been bickering over the tactics of the eight insurgents behind Kevin McCarthy's removal AFP

The overthrow of the US House speaker by a cabal of far-right agitators has left Republicans aghast at the party's chaotic approach to governing -- and its prospects for next year's presidential election.

Rudderless and wracked with division, the "Grand Old Party" (GOP) has spent the aftermath of Tuesday's historic removal of Kevin McCarthy bickering over the tactics of the eight insurgents behind the plot.

Meanwhile the rank-and-file has voiced little hope over the possibility of a new era of unity as talk of expelling the plotters adds to the sense of a party at war with itself when it should be in the trenches for American voters.

"Yesterday showed again the level of chaos within the Republican Party and the level of chaos that the Republican Party is willing to impose on the country," said political analyst and Princeton University professor Julian Zelizer.

"It creates great instability in the institution and the next speaker is going to be under even more pressure to placate the most radical elements of the party."

The House of Representatives, the lower chamber of Congress, is effectively leaderless for the first time in its history and in limbo, weeks ahead of a new funding deadline that could shut down the federal government.

Republicans will spend days -- possibly even weeks -- fighting over who they want as McCarthy's replacement instead of focusing legislative attention on the country's many challenges or even plotting victory in next year's presidential election.

Bookended by chaos, McCarthy's tenure began just nine months ago with extraordinary spectacle of a deeply divided party needing 15 rounds of voting to agree on its leader.

In the Senate, Republican watched with growing dismay as McCarthy was shown the door on Tuesday, worried by the threat to their legislative agenda that disarray in the lower chamber might pose.

"Today's action takes the attention off of President Biden's many failures and (puts) a spotlight on Republican infighting," griped South Carolina's Lindsey Graham.

Cross-party dealmaking was once the hard currency of US politics, but Capitol Hill is a more confrontational place than it used to be, populated by lawmakers hungry for the conflict that earns cable TV hits and fundraising dollars.

McCarthy's reliance on Democratic votes was a cardinal sin for an emboldened right wing allergic to compromise and in denial about what could be achieved when the Senate and White House are both controlled by the opposite party.

In a split-screen demonstrating Republican chaos across the board, and not just in Congress, former president Donald Trump spent Tuesday frowning darkly in a court that had already ruled that he committed business fraud for years.

This year alone, the Republican presidential front-runner has been found liable for sexual abuse and charged with 91 felonies over a cornucopia of alleged criminality.

"Here is a former president on trial again, and yet (he) remains at the forefront of his party's nomination race," Zelizer said of the civil fraud case.

"And you even have to have a judge trying to figure out how you restrain him from threatening and cajoling in public when he's also running," he said, referring to a limited gag order imposed on the former president Tuesday after he insulted a court clerk via social media.

Analysts credit the mercurial tycoon with showing more discipline than in previous White House campaigns, but his increasingly incendiary comments around his criminal cases have added to the image of Republicans as the mayhem caucus.

In recent weeks he has talked of executing a US military leader, mocked the 83-year-old husband of a leading Democrat after a brutal hammer attack by a home intruder and has called for shoplifters to be shot on sight.

Still, some analysts argue that Republican disarray is a feature, not a bug, as holding the feet of congressional leaders to the fire keeps them focused on conservative aims and makes the pain of occasional upheaval worthwhile.

Rob Mellen Jr., a political analyst and professor at the University of South Florida, expects Republicans to pick a unifying speaker in good time to deal with some of the most pressing challenges facing the country.

"The chaos in the GOP has not affected them in past electoral cycles and probably won't do so now... Americans also have a short memory," he said.

"We are still 13 months from the election and the cycle will have many more surprises before then."

Donald Trump
Former US president Donald Trump faces 91 felony charges AFP
Lindsey Graham
South Carolina senator Lindsey Graham complained that chaos was harming Republican messaging AFP