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

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.

In a new statement following the vote to remove McCarthy, House Democratic leader Hakeem Jeffries said, "It is our hope that traditional Republicans will walk away from MAGA extremism and join us in partnership for the good of the country."

Jeffries led his minority in voting against McCarthy along with the eight Republicans who ensured the speaker lost his role.

Separately, out of the White House, Biden press secretary Karine Jean-Pierre said the president is is hoping the House will "quickly elect a Speaker" and that he "looks forward to working together with them."

Rep. Patrick McHenry, a Republican from North Carolina, was quickly named as speaker pro tempore of the House on Tuesday after McCarthy was voted out.

What does that title mean? It's quite simply somebody designated to preside over the House when the speaker is unable to do so.

After September 11, the House adopted a new rule making it possible to have a speaker pro tempore even if the speaker of the House is unable to name one -- or the speakership suddenly becomes vacant.

The rule was adopted as a measure to ensure "continuity of government" -- so that Congress would not be paralyzed after a terrorist attack. A speaker pro tempore has the power to lead, to pass emergency measures and even a declaration of war.

The position is supposed to be temporary, but there is no explicit limit on how temporary or when a new election must be held to elect a permanent speaker.

But, for now anyway, Republicans are operating on the premise that the House can convene and function even without an elected speaker.

One thing driving the temporary nature of this situation: The speaker of the House is in the line of presidential succession; the speaker pro tempore is not.

-ABC News Chief Washington Correspondent Jonathan Karl