Would an Obama-Palin win have been possible?

My apologies for my ignorance, I'm not familiar with how the U.S. election process works, but here in the Philippines, it's not unusual for a popular Presidential candidate from one party being elected into office along with an equally popular Vice President from the opposing party, since the popularity vote is very much a part of Philippine politics and elections. From what I understand, the U.S. Electoral College system keeps the popularity vote in check. But my question is: Hypothetically, Could it have been possible for Palin to have beaten Biden and won alongside Obama given her seeming popularity? Or is there some sort of package vote for the party ticket to ensure this doesn't happen? If it is possible, how big a probability? A great possibility or once in a blue moon?