Assuming the House can successfully navigate these votes, the amended GOP plan would still increase the debt ceiling by $900 billion right away, and impose $917 billion in spending cuts over 10 years. But it changes the conditions of a second debt-ceiling hike.

The original bill allowed the president to certify that U.S. debt is within $100 billion of the new debt ceiling, after which another $1.6 trillion increase in the ceiling could take place. The original bill said this second increase would be conditioned on new spending cuts above $1.6 trillion.

But the modification adds another condition: that a balanced-budget amendment to the Constitution must be passed by the House and Senate and sent to the states before this second debt-ceiling hike can happen. This change is expected to bring along several Republicans who opposed the plan last night.

"It is time to stop pontificating and to start acting like members of Congress," Rep. Pete Sessions (R-Texas) said at the outset of the debate. He was countered by Rep. Jared Polis (D-Colo.), who again called on Republicans to abandon their plan because opposition makes Senate passage unlikely, and there are now less than five days until the U.S. hits the debt ceiling.

"I call upon the Speaker to move away from this direct and get back to the negotiating table to establish a real solution to reduce the deficit," Polis said.