When thinking about interesting PODs for the 60s, having a different Kennedy VP is a big one.
Completely changing Vietnam, the development of Civil Rights and the election in 1964, gives one an ample supply of available butterflies.
Smathers as Kennedy's VP is imho possible, he was a Southern Democrat and could have fullfilled a similiar function on the campaign trail.
Assuming that JFK is still assassinated:
How would Smather's act as President?
I assume, that neither Great Society nor significant Civil Rights progress is going to happen. And in Vietnam we will see an earlier escalation, possibly even an invasion of the North.