Republicans responded that the military spending bill — which, at $604.2 billion in the House version, matches President Obama’s budget request, excluding the contingency fund — was not the proper vehicle for debating sequestration. Speaker John A. Boehner of Ohio slammed Democratic leaders for backing away from the legislation since it passed out of the House Armed Services Committee in a 60-to-2 vote.

“I think it’s downright shameful that they’re even contemplating turning their backs on American troops,” he said.

Democrats were quick to note that Mr. Boehner had twice voted against the defense bill, in 2009 and 2010, when his party was in the minority. In the midst of the heated argument was one point of agreement: Sequestration, originally intended to resolve a stalemate over deficit reduction that began in 2011, continues to be an approach that pleases no one.

Senator Jack Reed of Rhode Island, the ranking Democrat on the Senate Armed Services Committee, was one of four Democrats Thursday who opposed moving the Senate military spending bill out of committee in a 22-to-4 vote. He offered an amendment that would set aside the contingency funding until changes were made to offer equivalent relief from the budget cuts to military and nonmilitary spending.