Actually, the minute Coleman is certified the winner, that's it—he succeeds to Wellstone's seat immediately under Minnesota law, with no input from The Body needed or allowed. The question is, what happens if when the election results are challenged. Theoretically, if the courts don't take firm action, it will be left to the Senate to vote on whether to accept Coleman or Mondale. Ventura has said that he will then appoint some third Minnesotan to temporarily fill Wellstone's seat, so that Minnesota gets two votes to determine the succession.
Now, yesterday the smart money said that Ventura's appointee would be a Democrat: firstly, because Ventura is left of center, and secondly, because it would have struck his sense of "fairness" as appropriate. However, it now seems likely that Ventura will pick either an independent or an outright Republican, rather than choose anyone connected in any way to last night's ghoulish carnival of hubris. So then things get really interesting. If the Senate maintains its current 51-49 balance of power, as seems likely (sigh), then whoever Ventura picks will in effect wield the deciding vote on whether to seat Coleman or Mondale.