For reasons that are off-topic to this question, McCarthy might lose a motion to vacate (some news are calling it a vote of no confidence, which is the wrong term); but it's clear that no other speaker can be elected.
So I'm left with the hypothetical that McCarthy loses the vote, is kicked out of speaker, and the house quickly finds they can't elect any speaker anymore.
Is this a deadlock scenario, or can the house pass bills (at least bills originating in the Senate) without a speaker?
Q: Can the US House function without a speaker?
For a while. There is a House rule for a vacancy in the Office of Speaker allowing the business of the House to continue until the election of a new Speaker.
Rules of the House of Representatives, 118th Congress
Speaker pro tempore
Rule I, 8 (3):
(A) In the case of a vacancy in the Office of Speaker, the next Member on the list described in subdivision (B) shall act as Speaker pro tempore until the election of a Speaker or a Speaker pro tempore. Pending such election the Member acting as Speaker pro tempore may exercise such authorities of the Office of Speaker as may be necessary and appropriate to that end.
(B) As soon as practicable after the election of the Speaker and whenever appropriate thereafter, the Speaker shall deliver to the Clerk a list of Members in the order in which each shall act as Speaker pro tempore under subdivision (A).
(C) For purposes of subdivision (A), a vacancy in the Office of Speaker may exist by reason of the physical inability of the Speaker to discharge the duties of the office.
The House Manual for the 118th Congress notes that —
A proposition to elect a Speaker is in order at any time a vacancy exists and presents a question of the highest privilege (VIII, 3383).
The first sentence in 8(3)(A) of Rule I allows the Speaker pro tempore to continue the business of the House. However, once a "proposition to elect a Speaker" has been made, that will take priority over other business.
Well, the first (and perhaps least obvious) point is the House sets the rules for the House. It's conceivable that the House could propose and pass a resolution allowing certain business to be conducted in the absence of a speaker. Neither party would want that, but if the speakership fight goes on too long there would be intense political pressure to find a resolution, and a bipartisan majority of reasonable congresspeople might take that route.
That aside, there is currently no mechanism for the House to operate without a speaker, which is why electing a speaker is the first priority of a new congress. The real problem is that McCarthy mishandled the whole situation. Part of the role of a speaker is to apply pressure to recalcitrant members of the caucus so that the majority party can effectively pursue its agenda. But McCarthy was so focused on becoming speaker that he reversed the dynamic: he allowed recalcitrant members of the caucus to pressure him into ceding power to their benefit. McCarthy wanted to avoid the stigma of a long, protracted series of speaker votes, but he should have embraced it, taking vote after vote for days (or weeks) if necessary until the recalcitrant members folded. By giving in he projected weakness and vulnerability, and the Gates, Jordan, Taylor-Greene faction are taking full advantage. If he does get vacated, we'll see if he learned the lesson, since he'll still be the most viable candidate for the position.
FWTW, according to CNN:
Republican Rep. Patrick McHenry of North Carolina will now temporarily lead the House of Representatives after the speaker's position was vacated on Tuesday.
McHenry, who is a top ally of Kevin McCarthy, was appointed speaker pro tempore.
His name was on a list McCarthy was required to give to the clerk in case of a vacancy.
The speaker pro tempore, which is the official title, can only recess the House, adjourn the chamber and recognize speaker nominations.
So, if that is right, it looks like the powers of the pro-tempore speaker [who was essentially pre-selected by the outgoing one] are fairly limited (for now). Possibly if the situation persists as such, the House might feel a need to increase those powers at his disposal.
Also FWTW, Deschler's precedents note this distinction between an elected and a designated pro-tempore Speaker:
An elected Speaker pro tempore is more than a ‘‘stand-in’’ Speaker. Indicative of this is the requirement that he swear a new oath upon his entering the office of Speaker pro tempore. Moreover, an elected Speaker pro tempore assumes a much greater scope of authority from The Speaker than a designated Speaker pro tempore. [...]
He must, however, be authorized by the House to perform certain duties even though he has been elected by the House, and not simply designated by The Speaker. Examples of the kinds of duties, powers, and functions assumed by an elected Speaker pro tempore from The Speaker include: administering the oath of office to new Members; (1) appointing conferees; (2) appointing committees to wait on the President and to inform him that the session’s work is completed; (3) or that a quorum of both Houses is ready to receive his state of the Union message; (4) signing enrolled bills and joint resolutions during the adjournment of the House; (5) declaring recesses during a session; (6) and presiding at a joint session of the Congress.(7)
However, McHenry has been designated rather than elected, so his powers appear indeed to be more reduced because of that.
There's another House Manual that notes that
When the Office of Speaker is vacant, the Member acting as Speaker pro tempore under rule I section 8(b) may exercise such authorities of the Office as may be necessary and appropriate pending the election of a Speaker or Speaker pro tempore.
However, it doesn't elaborate with any examples of what might be "necessary and appropriate" in such circumstances. Consequently Reuters concludes that
The acting speaker's duties are vague, according to a guide to the chamber's rules and procedures.
Anyhow, for practical purpose in this instance, they quote:
Republican Representative Kelly Armstrong told reporters that McHenry's main task will be to "get us a new speaker." Anything further, he said, would spark a move to oust McHenry.
Although I'm not exactly sure what makes Armstrong's view determinative in this case.
Also FWTW, there's the diametrically opposed opinion of some commentators that the speaker pro-tempore has full powers subject to the "support of the conference" (which is not too clear what it means--perhaps not getting vacated themselves).
Josh Huder, a senior fellow at the Government Affairs Institute at Georgetown University, wrote on X, formerly known as Twitter. "There's not [a] forcing mechanism for a new election, nor are there any overt restrictions on the power the pro tem would wield. The support of the conference would dictate the durability of this."
As that opinion doesn't reference any rules or laws, I'm guessing it comes down to a different interpretation of "necessary and appropriate" in the preceding discussion. (In doing so, it does seem to cast aside most if not all precedents from Deschler's though.)
