Democrats, led by Bill and Hillary, are going to try to put themselves in the position of trying to save ObamaCare. As Jesse Jackson might say, they want to mend it, not end it.
So, all these Democrats who voted for the bill, (and didn't know what was in it, obviously) are going to run as reformers of a law they put in place. Ordinarily, you might think it's an uphill battle. But with a complaint media, and so many low information voters, it's a strategy that might work. Underestimating the Democrats is like underestimating the devil himself.
Obviously Dems are in a much worse position now then anyone imagined they would be, with the website and the cancellations going together with Obamas past promises.
The way I would phrase what you are getting at is that even though Dems own this mess they will try to go to voters and say :
‘At least we tried to fix things with this reform and get the uninsured the health care they need.. Yes we are very frustrated with the rollout but we are trying as hard as we can to fix the bugs in this so the bill helps you. We are the only adults in the room trying to make things better. On the other side the GOP is just rooting for failure and trying to break things to make our President look bad”
For the time being the GOP should avoid bringing too much attention to themselves. Keep the spotlight on Dems.