The "To the Moon" speech was made in 1962 when we had basically no knowledge of space. We'd only sent a man into Low Earth Orbit for the first time a few months prior. 7 years later we'd land a man on the Moon. And we'd repeat this several times over until Nixon effectively cancelled the human space program in 1972. Obviously 7 years is not one day, but I think 1 day was clearly figurative rather than literal.

The biggest problem is that people have really lost the ability to think big. There's always infinite reasons to not do something, and there will never be a perfect time. So at some point you simply have to choose to push forward. Like Kennedy put it:

"We choose to go to the moon. We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too."