I don't know about primaries, I think they'd be kind of redundant. I've played over presidential race games that include primaries and it always just feels like something small to quickly get through in order to get to the core gameplay.\
Debates would really be awesome tho. Like the above poster said, it could be just like the interviews, but longer and more in-depth. Maybe have an "interrupt" button or something for when the opposing candidate is speaking.