Why did America fall in love with the universe in the 1960s?

I recently gave a presentation at school over NASA's budget, and I stressed the importance of having that budget increased. My arguments were solid, but my audience wasn't interested. It seems that most people are so distracted by things happening on Earth that the rest of the universe isn't even on their radar.

I could create a Kickstarter campaign today and raise a billion dollars for bedazzled Fitbits, but a manned space mission must be too abstract. In a place in time decorated with technology and innovation, it should be easy to capture the minds of the American people (especially the young) with space exploration opportunities.

I've put a lot of thought into figuring out just why space was so exhilarating in the 60s, but I just can't put my finger on it. Were generations before us more adventurous and ambitious? Did excitement from the Cold War cause Americans to feel more capable of accomplishing? Or, could it be that the publicity of space granted by presidents Kennedy and Johnson and their administrations ignited interest in the American people?

Why do you think America fell in love with the universe in the 60s, and what can we do to reignite that passion today?