Richard Nixon's opponent in the 1960 presidential election, Senator John Kennedy of Massachusetts, is not that well known, but he came very close to beating Nixon. By popular vote percentage it was the closest presidential election in history and really with a result that close, just about anything could have caused the election to go the other way. The Democrats made big gains in Congress two years earlier, so with that in mind it is even surprising that Nixon won.
What would a Kennedy administration have been like? One interesting fact is that Kennedy was Catholic, the USA still has not had a Catholic President.