Also Lieberman is an ass for running for re-election in 2000, instead of devoting his full energies to making sure that we didn't somehow have the worst President ever get into office. Lieberman's insistance on running for re-election was basically him saying he didn't think Gore would win.
I agree that I would have preferred him to step aside in 2000 rather than run for reelection; this also would have made it more likely that the Democrats could take control of the Senate (as it turned out, if Lieberman had stepped aside and Gore had won the White House, the Democrats would have controlled the Senate, assuming that the replacement candidate for Lieberman wins in Connecticut, which they likely would have).
LBJ ran for re-election to the U.S. Senate in 1960 while being on the ticket with JFK. There is historical precedent and on a winning ticket at that.