Many cabinet members from Eisenhower's Administration are crossing over into Nixon's including Labor Secretary James Mitchell and Attorney General William Rogers.
Well for one thing, the Bay of Pigs is handled better or called off, which that and Khrushchev knowing Nixon is not one to be toyed with, The Cuban Missile Crisis is averted. A watered down Civil Rights Bill is probably passed as well. With this, and with the economy recovering nicely from the early 60s recession, Nixon most likely wins another term in 1964. 1968 on the other hand, even if Vietnam is avoided, goes to the Democrats.