As Republican senators Ted Cruz, Mike Lee, Marco Rubio, and James Inhofe prepare to introduce a measure to defund Obamacare — and threaten to hold up a continuing resolution to fund the U.S. government if the measure is not given a vote — some conservatives are unhappy that the House, controlled by Republicans, did not do the same thing.

It wasn’t for lack of effort, at least on the part of some conservative Republicans. As the House prepared to consider its own version of the continuing resolution last week — it ultimately passed 267 to 151 — more than two dozen conservative GOP lawmakers signed on to an amendment that would have defunded Obamacare. They submitted the amendment and hoped it would receive a vote but were stymied when the House leadership declared that no amendments would be allowed.

“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. “They want desperately to take the idea of a government shutdown off the table,” says Salmon of the GOP leadership. “That message has been resonating loud and clear.” Although Salmon, who was in the House in 1995 during the last such fight — doesn’t want a shutdown, he nevertheless believes it “might be the only leverage we have with Obama to get to what we have to do, which is entitlement reform.”

For his part, DeSantis believes that if the GOP signals that it will do anything to avoid a shutdown, it will have little leverage to enact significant reforms. Obama, too, has something to fear from a shutdown, DeSantis suggested, if the public places some part of the blame at his feet. “If we don’t have a shutdown, that’s great,” DeSantis said. “I’m not advocating one. But at the same time, I’m not going to act like that would be the worst thing ever.”

“I don’t think we should ever take it off the table,” added Salmon. “I don’t have a trigger finger, where I’m itching to pull that trigger. But the fact is, we should never, ever say that all options aren’t on the table.”

House leadership sources did not respond to a request for comment.