Before it became clear how important political parties would be in the United States the vice president was the person who got the second most votes. What if this wasn't abandoned?
Well, not if you set up a running-mate system like they used in 1800. Of course, the Republicans screwed that up pretty badly IOTL, so it may not be as stable as I think.It was a really stupid idea in the first place, which is why it was abandoned almost at once.
Once you had parties, or even recognzed factions, the guy in second WILL be from the other party/faction.
You really want to encourage assassination as a part of the regular political process? Because you'd get that pretty darn quickly.