In fact, the chamber may be farther away. Kevin McCarthy, who has served as the party's House majority leader for four years, has 20 Republicans standing between him and the gavel - and they aren't budging.
Matt Gaetz, one of those so-called "Never Kevins", described Mr McCarthy as a "desperate guy" and said his request was simple: "For him to drop out of the race."
Mr McCarthy, for his part, pushed for the House to adjourn until Thursday, guaranteeing a third day of voting.
"I don't think a vote tonight will make a difference," he said, insisting that progress was being made. "But a vote in the future will."
With that in mind, here are three ways that future vote could turn out:
The current strategy from Kevin McCarthy appears to be to fight a war of attrition. His supporters will keep placing his name in nomination until those in opposition get tired of voting against him. Doing the same thing but expecting different results may be the definition of madness, but it may also be their only option until they can figure out what the recalcitrant Republicans really want.
If Mr McCarthy is able to craft some sort of deal, he would almost certainly have to offer more power and influence to his opponents, allowing them to declare victory.
The challenge for him is that any further concessions will ultimately weaken his hold on power, making it more likely that he could be unseated when the really tough fights - on things like the budget and raising the debt ceiling - take place later in the year.
Mr McCarthy could also hope that Democrats tire of the fight and stop showing up for the speaker votes, lowering the margin necessary for Mr McCarthy to win a majority. At least so far, however, Democrats appear to be relishing the Republican chaos.
And already, some Republicans - like Ken Buck of Colorado - are hinting that Mr McCarthy should step aside for alternative candidate, like his deputy, Steve Scalise of Louisiana.
Surrender has to be considered a possible, even likely, outcome for Mr McCarthy after two days of failure. At some point, the rank-and-file Republicans who are currently supporting Mr McCarthy may decide the best move is to give the hardline Republicans their scalp and try to move on. And if even a few of them break ranks, the floodgates could open.
"We're starting to get some open conflict on the floor as well as behind closed doors," Mr Buck, who has voted for Mr McCarthy all six times, said on Wednesday afternoon. "We have to choose a speaker and move forward."
Mr Scalise, the Republicans' chief vote-counter, is perhaps the choice best positioned to be a candidate acceptable to both the conservative hardliners and the rest of the House Republicans. He is considered a staunch, southern conservative and has literally bled for the party, having been seriously wounded in the 2017 attack on Republican members of Congress during a baseball practice. The biggest obstacle at the moment is that he doesn't seem to want the job.
Other possibilities include firebrand congressman Jim Jordan of Ohio and Jim Banks of Indiana, the head of the conservative Republican Study Committee. Neither seems capable of unifying the entire party behind him, however. (Byron Donalds of Florida was the nominee of the anti-McCarthy Republicans three times on Wednesday, but the novice congressman has been more of a vessel for ant-McCarthy sentiment than a serious candidate.)
Democrats and Republicans in the Ohio state House of Representatives joined together on Tuesday to reject a more conservative speaker and elect a moderate compromise candidate. Could such a thing happen in the US House of Representatives, as well?
There's been plenty of such speculation, as Mr McCarthy's predicament became clearer in recent days. Some of that has been fanned by his supporters as a warning for conservative hard-liners to fall in line, but some of it is real.
Don Bacon, a centrist Republican from Nebraska, has previously expressed an openness to working with Democrats to elect a compromise speaker if Mr McCarthy fails. Fred Upton, a former Republican congressman from Michigan with moderate credentials, has expressed an openness to presenting himself as a coalition pick (there is no requirement that a speaker has to be a current member of Congress). And there's been some talk of sweeteners for Democrats, like rule changes that would allow them to introduce legislation or more committee power.
All of this would require a sizeable number of Democrats to go along with the plan, which in today's sharply divided partisan environment seems unlikely in the extreme. And any Republican who works with Democrats will instantly be persona non grata among most conservatives.
Given that the House is already in uncharted territory by modern standards, however, no options are too far-fetched at this point.
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