Hi! What do you think would have happened had JFK not issued his manned lunar mission challenge -- say, because NASA and people like that argued that it was going to be extremely dangerous and expensive?
Instead, he does something else to compete with the Soviets (I don't know what though -- maybe space exploration, hanging around Earth orbit, etc. I can't remember how much had gone up on both sides when he made the speech).
Perhaps he decides to say "we'll cure cancer by the end of the decade" or something like that.