Kevin McCarthy says he now has enough support to become Speaker of the US House of Representatives, amid the deepest congressional dysfunction in more than 150 years.
The front-runner is building momentum on day four of the impasse, but he has lost 13 rounds of ballots despite his Republicans holding a majority of seats.
Fifteen of 20 or so holdouts changed their vote on Friday to back him, but six diehard dissidents remain.
The House reconvenes on Friday night.
After the 13th vote, as the lower chamber of Congress adjourned until 22:00EST (03:00 GMT), Mr McCarthy told reporters: "I'll have the votes."
In a remarkable turnaround on the 12th round of voting, Mr McCarthy was able to persuade 14 Republican holdouts to cast their vote for him. A 15th rebel followed suit for the 13th ballot.
But the California congressman was still three votes short of the 217 he needed to take the prized gavel.
The dissidents included members of the House Freedom Caucus, who argue that Mr McCarthy is not conservative enough to lead them as they work to stymie Democratic President Joe Biden's agenda.
Congressman Scott Perry of Pennsylvania said on Twitter he was switching to support Mr McCarthy after voting 11 times against him.
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"We're at a turning point," he said.
Two Republicans who missed votes earlier on Friday were flying back to Washington DC to cast their ballots for Mr McCarthy.
He has offered various concessions to the rebels, including a seat on the influential rules committee, which sets the terms for debate on legislation in the chamber.
He also agreed to lower the threshold for triggering a vote on whether to unseat the Speaker, to only one House member, leading to the possibility that the Republican coalition could easily fracture again even after Mr McCarthy's potential victory.
Meanwhile, the minority Democrats continued to vote in unison for their leader, New York's Hakeem Jeffries, the first black person ever to lead a party in Congress.
But it is highly unlikely he could win over any Republican defectors to garner the simple majority of votes in the 435-seat chamber needed to become Speaker.
Friday was the first day that Mr McCarthy's vote count actually surpassed that of Mr Jeffries.
Not since 1860, when the United States' union was fraying over the issue of slavery, has the lower chamber of Congress voted more than nine times to pick a speaker. Back then it took 44 rounds of ballots.
The Speaker of the House is second in line to the presidency after Vice-President Kamala Harris. They set the agenda in the House, and no legislative business can be conducted there without them.
In November, Republicans won the House by a slender margin of 222 to 212 in the chamber. Democrats retained control of the Senate.