Jonathan Chait says yes:
[B]oth chambers have already voted for a bill and set themselves up to be attacked for tax hikes, Medicare cuts and all the rest. The only chance the Democrats have to change that perception is to pass the bill, so that it can be explained in the context of success rather than as a tar baby subjected to endless criticism. If they let it die, they not only keep all the baggage of their votes, but they add a general stench of failure and profound demoralization of the base to their burdens. That would be a recipe not just to lose the House but to lose 50, 60, 80 seats.
Ross Douthat says no:
As of last night, the fundamentals of the situation have changed — and I don’t think that mulling things over for a couple of weeks will make House Democrats feel any better than they seem to be feeling at the moment about the possible costs of voting “yes.”I say: wait a minute! They aren't disagreeing; they're talking past each other.
There are really two questions each Member of the House will face: Do I want the bill to pass? Do I want to vote for it? Chait's logic is the logic of "Do I want it to pass?" Yes, I think it's correct that House Dems are better off if the bill passes than if it doesn't; Republicans are going to run against it either way, and without the bill passing there's almost no limit on what horrors they can claim for it -- while their Democratic opponents can't say anything, since doing so will get them into an argument they don't want. But Douthat's logic is also reasonable, because it's the logic of "Do I want to vote for it?" If the bill is unpopular in one's district, then (all else equal) it's pretty obvious that it's an electoral minus to vote for it. This gets to a conclusion that most House Democrats want the bill to pass, but without their votes.
That's the easy part. I'll talk more about specific groups of Members in Part 2.