Ah, I didn't know that! It makes perfect sense, when you think about it, though. It has ALL the earmarks of a Republican law, with some Democrat flavor thrown in here and there. It probably would have been good in hindsight to advertise it as a former Republican law (if they did, then advertise it more strongly, because obviously I knew nothing of its origins), though that could have alienated the Democrats. It would have gone a long way in keeping the criticism of it down to a manageable level, at least a level at which the Republicans wouldn't have been able to stymie it so easily.
I do like that Obama at least attempted to make it something that appealed to both sides. It's a testament to his promise to work on both sides of the aisle, though he hasn't always lived up to that historically (not that he hasn't made an effort, but even the best politicians can't hope to be completely apolitical).