Kevin McCarthy's replacement will inherit a poisoned chalice too

Watch: House Speaker Kevin McCarthy... 9 months in 90 seconds

Back in January, Kevin McCarthy struck a deal to become House Speaker that gave any one member of Congress the power to force a vote on whether to remove him.

On Tuesday, one Republican - Matt Gaetz - did exactly that. And, with the help of Democrats, he succeeded in kicking him out.

Now most Republicans are shaking their heads, wondering where they go next. All but a handful of them voted to keep Mr McCarthy in his job, but all it took was a few rebels to throw the chamber into chaos.

For months, Mr McCarthy had worked to keep his right flank in line.

He had agreed to open an impeachment investigation into President Joe Biden. He had backed away from a spending deal he struck with Democrats earlier in the year to raise the debt limit. He had let conservatives attach right-wing provisions to spending bills and other legislation.

All his efforts were in vain. When the Speaker relied on Democratic support to keep the government temporarily funded at the weekend, the die was cast.

Mr McCarthy could have still tried to win back power, cajoling or coercing the Republicans who sank him this week to change their mind, as he did back in January. But there seem to be few options left for him - and on Tuesday evening he indicated he would not run again.

The speakership that he sought for much of his political career has ended up a poisoned chalice - and, after the vote to oust him ended, he almost looked relieved, as fellow Republicans came up to shake his hand and give him hugs.

No matter which Republican replaces him, the divisions within the party will remain. And the challenges to effectively running the chamber are still the same.

That's because, while the moment was historic - the first Speaker removed by vote of the House - it also was the culmination of a fractious intra-Republican fight between the party's political establishment and its seething base that has been brewing since at least the Tea Party movement of 2010.

It's a fight between practicality and purity; between changing the system or working within it.

Watch: The moment McCarthy is removed as House speaker

Mr McCarthy barely won the Speaker's gavel back in January, as a handful of Republican rebels ultimately joined the rest of the party to support the California congressman. It was those final Republican holdouts who sunk the Speaker on Tuesday.

Although Mr Gaetz had allies who supported his "motion to vacate the chair", it was a decidedly one man show.

As Mr McCarthy's Republican defenders took turns standing during an hour of debate before the final vote, it was Mr Gaetz - positioned on the Democratic side of the chamber but talking to his fellow Republicans - who took the lion's share of the time to make the case against the Speaker.

What became clear was that both sides of the split within the Republican House think that Washington is broken.

For Mr Gaetz, it is the process by which federal spending is approved that is the biggest source of blame. He railed against how Congress approves massive spending bills for different parts of the federal government, which are often negotiated behind closed doors, then voted on in one large package.

He excoriated Mr McCarthy for making concessions to Democrats - who control the Senate and the White House - during budget and debt-limit negotiations and said if his party didn't take a harder line, nothing in Washington would ever change.

Watch: A timeline of the McCarthy-Gaetz feud

The Speaker's defenders, on the other hand, said compromise was part of the process - and that Mr McCarthy had been successful in advancing the conservative agenda.

Congressman Kelly Armstrong of North Dakota also pointed the finger directly at politicians like Mr Gaetz, who he accused of putting grandstanding and fundraising over governing.

"The incentive structure in this town is completely broken," he said. "We have descended to a place where clicks, TV hits and the never-ending quest for the most mediocre taste of celebrity drives decisions and encourages juvenile behaviour."

For the moment, the House is a broken institution - left without a Speaker and with no clear path to getting one.

With a jarringly loud gavel bang, the removal proceedings ended on Tuesday afternoon. Republicans, looking shell-shocked, retreated behind closed doors to figure out what to do next. Democrats, meanwhile, laughed and chatted - seemingly with the belief that this chaos will only work to their political benefit.

It's uncharted waters, however. And with the clock ticking toward a mid-November government shutdown, the waters could get very rough.