This is kind of an exaggeration. He "sold" the health care package to his own party. It was passed on a party line vote, with the sole Republican who voted for it doing so after it achieved the requisite number of votes and opposition wouldn't matter.

To the extent that Obama contributed to the health care passage it was by having a dark enough skin color to get an extraordinarily high turnout from a demographic that votes for his party 90% of the time, and thus managed to get 60 Senators so he could push anything through regardless of its popularity.