The basic point is that the probability that anything gets signed into law right now looks pretty low, and if anything does, it has to get watered down a lot to get through the Senate. Collins, Murkowski, Cassidy, Portman and the rest won't let anything even remotely like the old House version get through the Senate, and the House bill has already moved right. So, one of two things is the case: everything going on in the House right now is silly posturing over a bill that won't get signed into law, or everything going on in the House right now is silly posturing over a bill that will get moved in the opposite direction. Let's consider each possibility for the two sets of possible "no" voters in the GOP (assuming that mainline GOPers just vote "yes").
House moderates
Suppose the bill is just dead on arrival in the Senate, and like the Monty Python parrot, ain't comin' back. In that case, the moderates don't need to worry about whether the bill goes too far for them because it won't be enacted. They just need to worry about a) primary challenges (which are kind of a bullshit concern, but they think they need to worry), and more importantly, b) threats of punishment from leadership. So, just vote for the damned bill. In the alternative, meaning that the Senate will move the bill in the opposite direction, then it doesn't matter if the House version is batshit crazy because the Senate will do its job. Just vote for the damned bill. Either way, vote yes.
Hardliners
If the bill is dead on arrival in the Senate, then the point is merely to beat Paul Ryan into submission, making demand after demand that he is forced to meet, and then having someone to blame for failure. If the Senate is the chamber that votes no, then you get to blame the Senate for failure while treating Paul Ryan the way Donald Trump treats women, thereby feeling bigly about yourself. Hardliners just need a) lots of concessions, which they've gotten, and b) someone to blame, and as long as they can blame the Senate, they might as well vote yes, and call it another Obamacare repeal vote. Things only get complicated when they are forced to deal with a reconciled bill brought left by the Senate in the case that the Senate will pass some version, but just a much more moderate version. But, we aren't there yet. Right now, the simple thing to do is to vote yes, having already smacked Paul Ryan around.
What happens today? I don't know. Most of the time, over the long haul, the House majority party gets its way. This is Paul Ryan's first big test. If he passes, I'll be at least somewhat impressed, but as I said here, the incentives are on his side. The Senate, though? I said this to my classes yesterday, and I'll say it here. I regularly praise both Nancy Pelosi and John Boehner as remarkable and brilliant legislative leaders. The Senate is currently scheduled to vote on an Obamacare replacement next week. If McConnell can pull off a yes vote, next week, then move over Boehner and Pelosi. There will be a new master before whom we must all bow down. Republicans might pull this off, but to get it done next week?! That would be one of the most impressive political feats I've seen.