the only way this is going to be stopped now is if Google, Twitter, and the other big tech companies come out strongly against it. except for reddit, they've been quiet so far. don't count on Obama's veto threat at all.
His track record tells me he'll sign it happily while saying "I have serious reservations about this".
Libertarians are probably the weakest leg of the Republican coalition. The religious right and the neocons are much stronger, the former has little reason to oppose this, the latter might be naturally inclined to support it.
Interestingly, I've been hearing a bit about Democratic-leaning "civil libertarians" -- people who want small government without buying into any of the Republican social agenda. Maybe there's a way to build a coalition that can take a big enough bite out of both parties to force them to take notice...
Having your veto overturned is a bad thing. That alone would be a reason. The other reason being that Obama chose to stay silent on the SOPA/PIPA/CISPA issue the first time around. Coming out against it would have cost him relatively little in public opinion, which must mean there are interests relevant to him that aren't entirely opposed to the bill.
Happy to be wrong.