Well, not much change. VP's have very little power. The tax cuts in 2003 may not have passed in 2003 (although I am unsure how Lieberman voted on the tax cuts-he may very well have voted for them.)
Well Joe would have been replaced by a Republican since Connecticut has a Republican governor, so that guy would have definitely voted for the Bush tax cuts and thus no affect on most policies.
However, holy Joe wouldn't have been like disappearing dick. So possibly slight adjustments to our policy would have happened.