Nixon in 1960

[MATTROSE94]

I would say that the easiest way for Richard Nixon to have won in 1960 would be if John F. Kennedy selected Florida Senator George Smathers as his running mate instead of Lyndon Johnson. Considering that George Smathers was generally an opponent of civil rights legislation (with the exception of his reluctant votes for the 1957 Civil Rights Act and the 1965 Voting Rights Act), I think that Richard Nixon would have ended up doing about 5% better with the African-American vote (which would have narrowly swung New Jersey, Missouri, and Illinois into the Republican column). Also without Lyndon Joshnon on the Democratic ticket, Texas, New Mexico, and Nevada would have been narrowly won by Nixon as well, although Florida would have easily flipped to Kennedy due to the presence of Smathers on the Democratic ticket and several Southern states such as Georgia would have gone to Kennedy by an even larger margin than IRL.

[MATTROSE94]

A Democrat wins in '68 and likely '72. That means the GOP is likely to get stuck with the chalice that is the late '70's.

Not necessarily. It is possible that the Vice President of John F. Kennedy, who was elected in 1968 and easily re-elected in 1972 in this scenario, would win the Presidency in 1976. It is also possible that a Nixon victory in 1960 would either delay the Iranian Revolution (until perhaps 1983 or so), or prevent it from occurring entirely (I know that Nixon was a strong supporter of the Shah, so he may have encouraged the Iranian government to execute Ayatollah Khomeini and other opposition leaders during the 1963 Iranian protests), thus butterflying away the 1979 oil crisis and the Iranian hostage crisis.