Regarding the OP, whatever marginal benefit there may be in forcing the Dems to "own it" (I do not think there was ever any chance at all that the Dems would have sheepishly proposed an individual mandate delay, but who knows), I think is far more than countered by the fact that the debt ceiling fight wiped out the Obamacare launch failure stories in the news cycle.
There will still be some chatter about that as they try to get things fixed, but the GOP could have made a lot of hay over the failed launch. There were quite a lot of stories around October 1st with Republicans basically going "Oh God, this stupid Cruz stunt ruined our ability to scream about the launch"
how many emo kids does it take to change a lightbulb?
none they just sit in the dark and cry