“If that amendment had gone to the floor, far and above a majority of the conference would have voted for it,” said Arizona Rep. Matt Salmon, one of the supporters, in an interview Saturday. “I think everyone in the conference would have voted for it,” added Florida Rep. Ron DeSantis, another supporter.

Nevertheless, the Republican leadership did not allow the amendment to be considered. And that, Salmon, DeSantis, and other conservative Republicans believe, is a measure of the leadership’s uneasiness with continuing the legislative fight against Obamacare. Some Republicans — lawmakers who might have felt pressure to vote to defund Obamacare — believe privately that the fight is essentially over, and that the GOP should come to terms with the reality of national health care.

“I do think there’s a feeling in the conference among some folks who think that the 2012 election settled Obamacare, that we kind of need to move on,” said DeSantis. “I’m on the other side. I don’t think it did, because I don’t think it was a major issue in the campaign.”

The main reason that House leadership would not want a fight over defunding Obamacare was that it might scuttle chances of passing a continuing resolution, and thus bring up the prospect of a government shutdown.