Absolutely nothing. No danger of a World War, no danger of nukes. However, a number of things were operating on the Bay of Pigs.

First, it had been initiated by Eisenhower, the Supreme Commander in Europe while Kennedy was an obscure lieutenant in the Pacific. Kennedy was naturally deferential to Eisenhower's military expertise.

Second, Kennedy was assured by Bissel and Dulles that there would be a popular uprising against Castro. Just the opposite, the public spontaneously supported him. The Cuban refugees, just like the Iraqi refugees, spoon fed the US government pure nonsense hoping for an invasion.

And three, he truly screwed it up. Changed the plan with 4 days left altering it in ways which gave it no chance of succeeding even if there was public support, which there wasn't.

However embarrassing, that little sideshow was nothing compared to having the world on the line during the missile crisis.