Our POD is around the time JFK pretty much has the Democratic nomination wrapped up. So Jack is looking for a running mate, and he needs a Southerner, but instead of choosing old LBJ, he chooses Sen. George Smathers, a Conservative southerner from Florida. Smathers is interesting, he is a segregationist, but doesn't come off as one (sort of the opposite of LBJ) he's business friendly, and one of the signers of the Southern Manifesto.
No major butterflies, Kennedy/ Smathers narrowly beats Nixon/ Lodge.
Kennedy is shot on schedule, and Smathers is sworn in on Air Force 1.
Smathers is reelected on Kennedy's dead body in 1964.
So how does Segregationist Conservative Smathers react to the Sixties (Vietnam, Civil Rights)?
Does Smathers seek another term in 1968? Would he win? How could this impact the 1968 political realignment?