When you say "fiasco", I assume you mean an offshore nation that effectively resembles a tropical Nevada with sugar cane farms instead of ranches?
Don't forget that the '60 election was the beginning of the end for the Democrats' machine in Cook County (IL) and environs: despite voting every tombstone available, the machine still couldn't deliver for Kennedy. That produced a lot of alienated defectors. Had Kennedy won, well, that machine might still be alive and well.
One wonders how effective Kennedy might have been in getting civil rights legislation passed: as a northeastern urban Democrat, that may have been an uphill fight. Nixon as a western suburban Republican got cooperation that Kennedy might not have had. Don't overlook the return of sizable numbers of black voters to the GOP as a result of that civil rights legislation that might not have happened had Kennedy been elected.
One of the smartest moves Nixon made was dumping the ineffectual Lodge from the ticket in '64 in favor of Thruston Morton of KY. That was the beginning of a strategy that saw Republicans making inroads in the more moderate/progressive border states and upper south. Nixon's successor, SecState Nelson Rockefeller, was also wise in keeping Morton as his VP, and integrating him into the cabinet, similar to Nixon. Had Kennedy won, the south might well still be a solid Democrat province.