I think it would be good for Mitt Romney.
He can argue that Obama wasted a large part of his term working on a project that ultimately became nothing.
I think that would backfire because however people feel about the bill, they'd perceive that the SCOTUS, not the President, was to blame for its downfall and they'd see Romney attacking Obama over it as gloating, distasteful. After all, it would be Romney's side that go what they wanted, and it doesn't fit to attack the President for an outcome that Romney would support. Plus, I just don't think Romney would make this argument.
It doesn't affect the perception of Obama's priorities at all. He already took the damage from it while the bill was going through process.
And Obama can say that although it eviscerated the bill, he'll respect the Court's decision (and not pull an Andrew Jackson) and his administration would start rolling up the bill. The people would see that he respected the rule of law and the Court despite the deeply unfavorable ruling to him.
Basically, the practical effects of the ruling and the massive size of the law, including the vast portions that have nothing to do with the mandate, have so far been low key. If they struck down those portions the debate would be focused on that, and the public would be focused on the more popular provisions that were struck down. Obama could then argue that the Court massively overreached and plead against a radical Republican takeover of all four branches of government, which would be effective. America is still a relatively centrist country.