Kerry does better than Lieberman in the debate, and the home-state effect, combined, are enough to put N.H. in the Democratic column. Gore/Kerry wins 271-267. However, Kerry is not Jewish, so Bush wins by a much larger margin in Florida. The outcome is the opposite of RL: Bush wins the popular vote, Gore wins electoral.
Thus energizing the Republican base (and bringing many young and unintelligent voters to the GOP) leading to a close win in 2004 under the assumption that Gore cheated.
However, this would be a small consequence, as real life probably would've asserted itself anyways, with the GOP being blamed for the recession by the general public, leading to a Dem victory anyways in 08.