By Alex Rogers
August 1, 2014

Updated at 3:12 p.m.

One day after the House Republican leadership pulled its bill to address the ongoing border crisis, it appeared to garner enough confidence to put an altered version on the floor.

Rep. Steve Womack (R-Ark.) called the move “a classic case of measure twice, cut once.”

“Quite frankly I personally believe that the model that we gave yesterday—as messy as it appeared to all of you guys—was probably a very good model,” said Womack, a member of the Whip team who says he appreciates the new leadership’s “bottom-up” approach. “We took a step back, we evaluated and engaged our colleagues and came up with a piece of legislation.”

The House Republican leadership introduced the new bill to the House GOP conference in a Friday morning meeting in a room beneath the Capitol. The $694 million bill doubles the amount of National Guard funding for border state governors to $70 million, according to a senior House Republican aide. Since only Texas has authorized National Guard deployment, that pot of money could all go to the Lone Star state. The extra $35 million would be offset by Department of Defense cuts.

There are also a few policy changes. One amendment tightens up language regarding the adjudication process for unaccompanied minors. Many of the over 57,000 children who have come over the southern border illegally since October are from Honduras, El Salvador and Guatemala, and the House bill would treat these children similarly to Mexican children, who are screened and deported faster than those from Central America.

In a nod to conservatives, Rep. Marsha Blackburn (R-Tenn.) told TIME that she will get a separate vote on her resolution that would block President Barack Obama from expanding the Deferred Action for Childhood Arrivals (DACA) program, a move immigration activists expect Obama to take later this year. DACA, enacted through a June 2012 executive order, grants two years of deportation relief to qualifying illegal immigrants who came to the U.S. as a minor. Blackburn added that the “logistics” of the vote are still being worked out.

Notably, hardline conservatives Reps. Steve King (R-Iowa) and Michele Bachmann (R-Minn.) support the border bill, according to their respective spokespeople. Rep. Dana Rohrabacher (R-Calif.) told TIME that in the conference meeting, Bachmann said, “I may have said ‘Hell No’ yesterday but I’m saying ‘Hell Yes’ today.”

“That’s very impressive, you know,” added Rohrabacher.

The bill for all practical purposes doesn’t matter, as it won’t pass the Senate, which failed to pass its own $2.7 billion border bill Thursday night. But for House Republicans, addressing the border crisis with their own bill is important enough that they skirted a 1970 law mandating that the chamber go into recess in early August. Most Senators have already left the capital, while their House colleagues are expected to do the same shortly.

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