The looming vote to lift the federal debt limit marks a crucial test of strength for House Speaker John A. Boehner as his allies scrambled across Capitol Hill on Wednesday to line up votes ahead of Thursday’s floor showdown.

Rep. Steven C. LaTourette, an Ohio Republican, said about 20 of Boehner’s top lieutenants gathered Tuesday evening in the speaker’s office to plot a path to passage. Some reluctant conservatives, many in their first term in Congress, have been slow to embrace their leader’s package, hoping to hold out for more concessions from President Obama and the Democrats.

A morning meeting of the GOP caucus on Wednesday yielded some momentum for the speaker, several GOP lawmakers said.

“It was a little bit like an altar call today at conference,” LaTourette said of the closed-door meeting. “There were members who stood up – they were no [votes] or undecided, and they’re going to be yes [votes]. That will continue as more people come to the Lord.”

Boehner needs all but two dozen of his members to ensure passage of his plan. Already, nearly a dozen Republicans have defected from the GOP leadership’s plan, including Rep. Michele Bachmann (R-Minn.), a presidential contender.

But boosting its chances was a new analysis of Boehner’s revised plan from the nonpartisan Congressional Budget Office. The speaker’s office said it meets a key test for conservatives, that spending cuts match or exceed the amount of the requested debt limit increase.

This afternoon, Boehner huddled with the influential freshman class at its weekly meeting. At one point, House Majority Whip Kevin McCarthy (R-Bakersfield), who is charged with corralling votes, bounded in like a high school football coach set to rally his team. He clapped his hands together as he quick-stepped up a short flight of stairs into the Capitol basement room.

He declined to comment on his efforts to line up GOP support.

Boehner’s plan, which would trim $917 billion in federal spending over the coming decade, faces an uncertain future even if it passes the House. The Obama administration has threatened a veto, and Democrats who control the Senate are ferrying through an alternate proposal.

That makes Thursday’s vote a crucial political statement of support for Boehner. LaTourette said he was mystified that some of his GOP colleagues seemed to believe that “somehow, magically our leverage increases after Aug. 2,” the deadline to raise the debt ceiling before triggering a federal default.

“I am actively recruiting Republican candidates who are psychiatrists to run in 2012 elections,” he deadpanned.