No way a young Texas Governor wins the Democratic nomination in 1960 and defeats Nixon in the general election.
In 1960, the Cold War was the issue that was on most of the electorate's minds. Nixon campaigned on the issue of experience, even though he and Kennedy entered politics in the same year, 1946. Nixon claimed that, as Vice President, he had the upper hand when it came to dealing with the Soviet threat. Kennedy was also an ardent Cold Warrior, claiming that under Eisenhower, we had incurred s "missile gap" with the Soviets. There were virtually no potential candidates running in 1960 without foreign policy experience. Even the two Governor non-candidates (Stevenson and Rockefeller) stressed their foreign policy experience.
I pretty much agree with this. As a governor, Connally can't credibly claim a missile gap. (at least JFK was a member of the Senate, so he could claim to know the numbers) I also don't think Joe Kennedy would have put his money to use as he did with JFK at the top of the ticket. I also think Connally chooses a more seasoned running mate to offset his youth & inexperience. Being from the south would have cost the Democrats northern black votes, which were crucial to Kennedy's victory as well. Plus Nixon won't look as bad standing next to Connally as he did next to Kennedy.