Republican Liberal

It puzzles me that Bush and gang are throwing their support to Joe Lieberman from Connecticut rather than supporting the Republican candidate. I mean wasn't Lieberman a liberal... a Democrat? Did the Democratic Party nominate Lieberman to be the candidate for Vice President in 2000 because they knew he wasn't a liberal Democrat?
So if he was a liberal and supported things like pro-choice and gay rights, what effect will this new White House campaign to reelect him have on the Religious Right's support for Bush?
I think Karl Rove owes them an explanation.