(A comment I made over at io9 as well.)
As someone who lived through the ‘false dawn of space travel’ (to use Heinlein’s phrase), who grew up intensely following the space program, and who actually worked at NASA/JSC on the Space Shuttle flight simulators back in 1979-80, I can give you my observation: the American people got bored with space. Seriously. No one (outside of a small group of space enthusiasts, such as myself) was clamoring for yet more Apollo missions. TV ratings of flight and moonwalk coverage sank to the basement. It was all just more men in space suits skipping around in a black-and-white environment.
With no public demand or support, neither Congress nor the White House had much stomach for pushing things forward, not when the funds had other uses. The NASA manned flight division evolved into a jobs program, which is why NASA fought against privatization of space flight for so long. (The NASA unmanned space exploration division continued to work miracles, even as it does to this day.)
Of course, the real root problem was that the Apollo approach was fundamentally flawed in the first place; as some wag put it decades ago, it was like building a cruise liner for a single crossing of the Atlantic and sinking everything but one lifeboat at the end of the trip. Prior to Kennedy’s challenge, the US was working on an incremental approach: SSTO (single stage to orbit), gliding re-entry, and a space station. We basically lost half a century due to the Apollo approach (and the horribly expensive, horribly fragile kludge that was the Space Shuttle). Frankly, NASA’s current Orion effort is a repeat of just about all the mistakes we made with Apollo and threatens to soak up NASA’s budget for years to come, even as goal dates keep getting pushed back more and more.
The night that Apollo 11 landed, I was part of a group of friends (we were all high school students) who stayed up all night to watch the coverage. When I heard the words, “Houston, Tranquility Base here. The Eagle has landed.”, I felt the future had begun. I was sure I would live long enough to visit LEO myself and to see humans colonize the moon and land on Mars. If you had described to me back in 1969 what the state of space exploration (and, in particular, US space exploration) would be in 2015, I would not have believed you. And yet here we are.