With the Vietnam War expanding, civil unrest, riots in the streets, and racial tensions at home, America turns to Nixon for new leadership after 8 years of Democratic administration.
In 1968, Nixon is seen as offering new leadership, not more of the same. Sorry, JFK, but 1968 would simply not be your year. 1960 was your best chance.
Mike Mansfield is an excellent Vice Presidential pick for Kennedy, as far as leadership quality, but does not bring in the Republican west for Kennedy. The Montana icon brings Montana into the Kennedy column. (I know this is unrealistic, but I am giving Mansfield the benefit of the doubt as to whether he could swing Montana from it's solid Republican voting pattern)
Too bad Nixon didn't choose better than Agnew.
Wallace and LeMay hold much the deep south.
Nixon wins a fairly close contest.
Nixon/Agnew 281
Kennedy/Mansfield 212
Wallace LeMay 45