Lieberman Tie-Breaker?

Let's say that the it turns out that Webb wins two weeks hence (recount) and the Senate is 49/51. Lieberman says that he plans to caucus with the Democrats, but will he? Desperate Republicans would urge him to pull a Jeffords and promise to give him whatever committee chairmanship he wanted. That way the Senate is 50/50 and Vice-President Cheney breaks the tie. On the other hand Webb could just lose and we will be not change this particular channel on our long national nightmare.