A big cause of waning public enthusiasm in space is, I believe, that it all still looks like the 60s. The ships look the same, the suits look the same, the propulsion technologies look the same, and what's worse... we can't even DO the cool stuff we could do in 69!
If you had asked someone in 69 what spaceflight would look like in 2012, they would probably have visions of Moon bases, space stations with gravity wheels, and routine manned trips to Mars.
But we have none of those things. Instead, we have a recently-retired space truck, a space station that looks like a larger version of Skylab, and all of this stuck in low Earth orbit.
How. Incredibly. Disappointing.
I want to get excited about space again. I really, really do. The recent gains made by private companies (with Scaled Composites in '04 and SpaceX today) have helped a lot. But we shouldn't shy away from bigger ideas.
I know it sounds silly to people in the space business, but the public could really use some futuristic looking space ships and more exciting missions to get excited again.
In the end, I believe that private industry will make this happen once space tourism becomes more affordable (simply because the different companies will have to start competing on something other than "look, we're in space!").
Bigger, cooler looking space ships that are built in orbit and make regular trips to and from Mars would be REALLY exciting. It doesn't have to look like the Enterprise. What about a small Klingon Bird of Prey or even a UFO-style flying saucer?
So, no, we don't need to build the Enterprise, but we DO need to take this as a marketing lesson about why the public seems to yawn when they hear anything about space and Nasa these days.