Apollo was a result of Cold War politics. Helped on the margins by the desire of LBJ and other Southern Democrats to funnel government money into creating high-tech jobs in what was then a region significantly less developed than most of the nation.

No Cold War, no pork, no Moon, that simple.

Once we were going science did become part of the project but science would never, ever have generated a program that big.

Vietnam had a marginal role in killin Apollo, in that it was part of (but not entirely) the reason for the budget squeeze and high inflation of the early 1970s, and for increasing distrust of the government generally.

Even without Vietnam, it's not at all clear why public/Congressional support would have continued -- it was already waning significantly by 1968. The success of Apollo 8, the busy and exciting run up that spring, and then the glory of Apollo 11 (four dramatic flights in seven months!) perked it up for a while, but there was nothing at all to sustain it once we reached "task accomplished".

I suspect there might have been a more serious challenge to Apollo had Kennedy lived. The association of attacking Apollo with attacking a slain president's memory made it harder to take on.

That being said, NASA could have saved Apollo 18 and even had a shot at 19 or 20 if it really fought hard for them. GB is right on about the "let's quit while we're ahead" mentality, and the drive to forget Apollo and move on to Shuttle. With 18 especially it was a NASA decision, not Congressional pressure.

On a side note, it didn't help that the scientific community at large never warmed to Apollo, even after the successes of 15, 16, and 17. Given how little extra money 18 would have needed a lobbying push by the scientific establishment would have helped, but they (on average, not all) focussed on pushing unmanned probes and generally grumbling about astronauts.