There was considerable thought on him becoming John Kerry's running mate in '04. He and Kerry have always been big buddies and with his somewhat moderate social stances and his general dislike for Bush, it almost became a reality. and guess what.....that ticket would have won.
I think the day might be coming where we will have a ticket with one candidate being a dem and one a republican.
Another side note....you read it hear second....I saw it in the paper the other day. If, and its a big if, Obama gets the dem nomination, look for him to choose Bill Clinton as his running mate. The law does not prohibit a former president from being a vice president. I know it sounds far fetched, but do not think it won't be considered.