Ike was really a Demonrat. Because of Truman’s massive unpopularity (akin to Wilson in 1920) he didn’t want to run as one because that would’ve stood a good chance of him losing in 1952 (it should’ve been Robert Taft & Gen. Douglas MacArthur as the GOP ticket). Ike’s father was a Socialist.
And, yes, he did nothing at all to help Nixon in 1960. Had he dropped dead from one of his heart episodes before 1961, that would’ve elevated Nixon and he would’ve, again, handily won that year (somewhat similar to 1964).
The lefties/Pinkos/stinking COMMIES/Fellow travelers had been after Nixon, too and claw, unceasingly, since he beat Helen Gahagan Douglas, for the Senate Seat. And Ike did less than NOTHING WHATEVER, re that whole thing and the crap thrown at him, resulting in THE CHECKERS SPEECH!
Yet through it all, Nixon never bad mouthed Ike, when it happened, or afterwards.
Ike's help, in '60, might have helped; however, what with the Mafia and Dem rigging, who knows?