That's the potential problem for which there's no potential Plan B.
As a matter of politics, I have little doubt that even for Dems in marginal districts, it's actually the safer call for them to vote for the bill a second time. Because the key is they already voted for it once. And from a strategic position in their districts, that is all that counts. Saying, 'yes, I voted for it but, hey, when it came back from conference I refused to vote for it again and it never came to a vote and the legislation died!' just ain't a distinction anyone's Republican opponents are going to allow.
I suspect it won't even cut it for those who actually voted no the first time. But it definitely won't work for those who already voted for it once. That's the lesson of 1994, the conservative and moderate Democrats who killed health care reform derived not an ounce of benefit for having done so. Indeed, they were slaughtered en masse.
I have very little doubt that that analysis is correct. But that doesn't mean the members in question will see it that way.