A switch of two large swing states in the 1960 election would have given a decisive victory to Nixon. Those two states were Texas and Illinois.
Take the dead vote out of Illinois (and more specifically, Cook County, where Kennedy got 110% of the population in several Chicago wards to vote for him) and the state clearly went to Nixon.
Take the illegal alien vote out of Texas (and most specifically, the border counties and urban areas) and the state clearly went to Nixon. Kennedy put Johnson on the ticket because he was paniced that the "old solid south" had started to crack under Eisenhower, and he was right. Nixon won the Anglo vote in Texas overwhemingly...check all the election data from that year.
Think how different the world would be, if Nixon had become president then , instead of JFK !