Well, it's not impossible, to have Ted Kennedy run in 1992. It's not like he was that old, and Bush and Reagan were no spring-chickens, either.
As for a Republican -v- Democratic contest, I suppose you could have Clinton switch to the Republicans for political expediency in the 1980s, although I don't know how successful that would be. After all, Clinton wasn't always a blue dog - he ran McGovern's 1972 campaign in Texas.