House Republican Leader Kevin McCarthy seems all but certain that he has the votes to push this over the finish line tonight.

"I'll have the votes," McCarthy said as he headed off the House floor after the chamber adjourned until 10 p.m.

"We'll come back tonight, and I believe at that time we'll have the votes and finish this once and for all," he said.

McCarthy attempted to portray the drawn-out negotiations and multiple ballots -- the most since before the Civil War -- as a positive thing. "This is the great part," he said. "Because it took so long now we learned how to govern."

But to be clear, this is still a bit of a numbers game and McCarthy doesn't have the votes yet.

He still needs to flip votes. If there are zero absences , McCarthy would need to flip two of the six remaining holdouts: Reps.-elect Andy Biggs, Lauren Boebert, Eli Crane, Matt Gaetz, Bob Good and Matt Rosendale.

But there are other paths to the speakership, again assuming no absences when members reconvene: Either one flips of remaining holdouts; one flip and one (or more) "present" votes; if no flips, three or more "present: votes.

Asked by ABC News what he says to those who think he's giving up too much to a small percentage of his conference, McCarthy argued that it was actually the whole conference that came together on these reforms.

"The whole conference worked on these reforms. These reforms are actually very good. It empowers the members," he said.

--ABC News Katherine Faulders, Lauren Peller, Will Steakin and Ben Siegel

At this point, House Republican leadership expects Republican Reps. Ken Buck and Wesley Hunt, both McCarthy allies who are not currently present, to return to Washington sometime this evening for another round of voting.

The House has voted to adjourn until 10 p.m. as those Republicans make their way back to Washington.

Upon their return, if all votes remain the same as the last ballot, McCarthy would have 216 votes, leaving him two votes shy of the speakership.

That means McCarthy would need to flip two of the following holdouts to win: Reps. Andy Biggs, R-Ariz., Lauren Boebert, R-Colo., Matt Gaetz, R-Fla., Bob Good, R-Va., Rep. Matt Rosendale, R-Mont., and Rep.-elect Eli Crane.

-ABC News' Trish Turner, Katherine Faudlers, Lauren Peller and Will Steakin

Rep. Andy Harris of Maryland appears to be the only remaining holdout Republican to flip his vote for McCarthy so far in the 13th round of voting, signaling more momentum for McCarthy but not enough to win the speakership.

While no other Republican was formally nominated this round, five voted for Rep. Jim Jordan, R-Ohio.

Reps. Andy Biggs, R-Ariz., Lauren Boebert, R-Colo., Matt Gaetz, R-Fla., Bob Good, R-Va., Rep. Matt Rosendale, R-Mont., and Rep.-elect Eli Crane remain in the "Never Kevin" crowd.

Rep. David Trone, D-Md., is back on the House floor for this 13th round of voting.

Assuming he does vote, that will bring support for Rep. Hakeem Jeffries to 212 votes and the total number of votes cast to 432. That would mean the new magic number McCarthy would need to win the speakership is 217 votes -- four more than he got in the previous round.

--ABC News' Rick Klein