The measure would require that $85 billion in spending be cut, but give President Obama more flexibility in manage the spending reductions than given by the sequester, which requires across-the-board cuts to nearly every part of every agency.

But some Republicans fear it would help the White House use the cuts as a political weapon, while defense hawks worry the Pentagon would not escape harm.

Sens. Lindsey Graham (R-S.C.) and John McCain (R-Ariz.) said the plan doesn’t address the damage that the sequester cuts would inflict on the military.

“I don’t care how flexible you want to be, the top-line numbers don’t add up to me on defense. That’s my problem,” Graham said after a contentious GOP meeting where the plan was discussed.