If you look down in the comments section, several people have posted the relevant laws. It seems that Bayh would need to wait until Jan 13th to resign in order to let Long-Thompson appoint a replacement (of course this totally assumes she beats Daniels).
____________________________________________________________________________________________________________________________
Shadow Senate Race?
Just to tie together couple of things from yesterday: suppose that Barack Obama picks Evan Bayh as his running mate. Suppose this ticket wins. Do the Democrats lose a Senate seat?
Actually, it's not so clear. The Governor would get to make a two-year appointment if Bayh had to resign his seat, with a Special Election to be held in 2010. The present governor of Indiana is Mitch Daniels, a Republican. Unlike some states -- Arizona, for instance -- Indiana does not appear to have any requirement wherein a gubernatorial appointee must pick a candidate from the departing Senator's party.
But would Daniels still be Governor at the time Bayh resigned his seat? He's in a quasi-competitive race with Jill Long-Thompson. I'm not entirely sure how Indiana elections law works -- this is one of those instances where Google fails you --but I'd assume as a default that the incoming Governor would get to make the appointment (there's only a 49.99 percent chance that I'm wrong about this). If this whole parlay plays out, you could have a two-birds-with-one-stone, de facto Senate race in Indiana based on the gubernatorial result.
In any event, we have a very boring set of gubernatorial races this year, but Indiana is one that the Democrats ought to consider pouring some money into (and Republicans likewise to defend their incumbent). It's a state that has long been redder than it "should" be based on its demographics, and where there might be some long-run benefits to building out the party's infrastructure.
-- Nate at 4:50 PM
http://www.fivethirtyeight.com/2008/07/shadow-senate-race.html