I think the chances of it are very slim or none. The conditions for it in 1981 included a closely split Illinois Senate and a Governor of the other party. The Senate Dems currently have a veto proof majority and are expected to hold that if not build a bit on it with Obama on the fall ballot.
Just today, it would take 8 Democrats to switch and in 1981, that wasn’t the case. The only reason the Republicans could pull it off was that there were two absent Democrats in a Senate divided 30-29 and Thompson gave a questionable ruling that it wasn’t a Constitutional majority that was required, but a majority present. As Rich notes, the current Senate rules require a Constitutional majority (30 votes).
One other time it happened, but I don’t know the history on that.
My sense is that Blagojevich will try and find a way to install a friendly Senate President in some sort of move, but that he’ll fail. Much of his own party hates him and the Republicans hate him even more in the Senate. Hence, my point that he is delusional, but you can bet he’s trying to come up with some outrageous scenario in his head–something out of sport talk radio where the Cubs offer up Dempsey and a player to be named later for Johan Santana.