You could go the Red Dwarf way. Kennedy doesn't get assassinated but gets involved with a mob boss's girl. The scandal rocks the country and he gets impeached. J. Edgar Hoover is forced to run by the mob (which is blackmailing him with pictures of Hoover in drag at a gay club) and wins. Later he's forced to allow the Soviets to put nuclear missiles in Cuba in exchange for trade rights in drugs. With active Soviet missiles so close to the US, people flee the major cities/country in droves, and the economy crumbles.
Best episode of the whole damn show.
Kennedy was the 2nd gunman on the grassy knoll.