The mistake many people make is thinking that that success can be repeated merely by giving money to NASA. The success of the Apollo program as an incubator of scientific and engineering accomplishment was directly tied to both the sense of mission that the participants felt, and the fact that it was widely perceived as a race with a rival power with potentially apocalyptic consequences for losing.
It's not categorically impossible to create that sense of mission anew, but recreating the overall context would be difficult. The closest we've seen to public programs that capture the competitive juices of the participants are contests like the DARPA robotic vehicle challenge.
As I stated above, I think the Apollo missions were unique in their historical context and unlikely to be repeated as a model.
It's one of those tired old saws that everybody believes, but I never bought.