Eisenhower would pick Knowland, who's dumb as nails and a China Lobby tool. Ike disliked Knowland since he (rightfully) considered him unintelligent and obsessed with Jiang's ChiNats on Taiwan. If Knowland is nominated in '60, JFK in a walk, even many Republicans would vote for him not just because it's almost Palin v. Obama but the domestic ideological differences between JFK and Nixon (to say nothing of the proto-DLC Bobby) IOTL were practically non-existent, both being firm centrists. It's a matter of public funding/private funding for shared liberal goals. Without Nixon the GOP would nominate Goldwater in '64, and in '68 the closest Nixon analogue would be George Romney. He'd lose badly to Humphrey, and Bobby (if things go similar to OTL, but he lives and is nominated) would kick his ass in the general. There were quite a few 1967 polls that showed RFK beating Romney 55-39. So that's up to '68, after that depends on the butterflies. Also- there is a decent possibility that RFK becomes a Republican. In the early-to-mid '50s it is really only family loyalty that would prevent it, not ideology. Without the Hoffa business, somewhat more likely.
Now, Nixon continues being the Zinn/Chomsky analogue until he dies sometime in the '90s. Actually, I think Nixon would wind up as the ATL Zinn myself, perhaps even writing a similar book to APHUS.