Amid House speaker vacancy, many in GOP want to do away with motion to vacate

Now-former Speaker McCarthy addressed reporters from Capitol Hill on Tuesday night where he looked back at his years in Republican leadership, touted his record -- and struck an optimistic if ambiguous note about his future.

"I believe I can continue to fight," McCarthy said, while noting that he will not run again for speaker after he lost a historic vote on the motion to vacate earlier in the day.

"My goals have not changed. My ability to fight is just in a different form," he said, later adding, "I'll never give up on the American people. That doesn't mean I have to be speaker."

McCarthy also swiped at the conservative rebels who ousted him from his role -- stressing that they were just 4% of the GOP conference -- and claimed that Gaetz was acting out of a personal sense of grievance in pushing him out, which Gaetz denies.

Despite the defeat he suffered from within his own party, McCarthy sounded largely sanguine about his political career.

He contended that the Democratic minority deciding to vote against him had made a "political decision" that undercut the ability of the House to govern.

"My fear is the institution fell today," he said.

Still, in largely valedictory remarks, he pointed back to work to cut government spending, expand his party's base and increase their majority in Congress, including by electing more women and minorities.

"I feel fortunate to have served the American people," he insisted. "I leave the speakership with a sense of pride, accomplishment and, yes, optimism."

-ABC News' Adam Carlson

The House has canceled votes for the remainder of the week, according to Majority Whip Tom Emmer.

GOP sources say that Speaker Pro Tempore Patrick McHenry told party members during a Tuesday night conference meeting that the House is expected to recess until Oct. 10 -- and the plan is to hold a speaker candidate forum that day and then a vote for a permanent speaker on Oct. 11.

House Majority Leader Steve Scalise appears to be emerging from the closed-door conference meeting as the front-runner to replace McCarthy.

Both House Republican Conference Chair Elise Stefanik and Emmer indicated they're not running for speaker.

It's unclear if Scalise has enough support to succeed, but he spoke to reporters as he walked back to his office.

"We have a lot of work to get done, but I haven't made any formal announcement," Scalise, R-La., said.

"Clearly within our conference, we have a very tight majority," he acknowledged. "Getting things that done is going to be difficult in the tight majority. It's still will be so no matter who's going to be the next speaker, the challenges still remain, but I think the opportunity is there to continue moving forward."

Asked whether he is physically up to the job as speaker as he continues treatment for blood cancer, Scalise said, "I feel great."

In a closed-door meeting on Tuesday night, McCarthy told fellow Republicans that he will not run again for the speakership, per multiple sources in the room.

He also said that when the next vote comes around for another speaker, Republicans should try to elect that person on the first round -- and if he had to be the sacrifice, so be it. McCarthy thanked those who supported him.

On his way to the party meeting, McCarthy told ABC News' John Parkinson, "Life goes on. You never give up."

Ousting McCarthy -- a push first launched by Republican hard-line Rep. Matt Gaetz, embraced by seven conservative colleagues and helped along by Democrats who declined to save McCarthy's job -- was a long time coming.

One could blame the debt and spending agreements he cut this year to keep the government open and to keep the country's credit intact; or the side deals reached to allow him to become speaker in the first place; or the slash-and-burn political styles that have become the new normal of Congress.

But in the end, what happened on Tuesday never happened before because there's never been a dynamic quite like the one now inside the House Republican conference or inside the GOP writ large.

Read more from ABC News Political Director Rick Klein's analysis here.