If you were to ask any person what they thought US's most notable achievement was - it's not unlikely they'll mention the moon landing. The moon landing was such a milestone, such a landmark achievement - it sent nationalism through the roof. That kind of pride and fervor would be extremely over the next few years, not only in economic recovery, but in growth and expansion of tech related fields.
All it would take is one very good speech I think, to inspire the nation and light the fire under US's latent tech reserves. Something kinda like Reagan's speeches - which felt like pep talks more than presidential speeches, linking the economic, political, and cultural muscle of America's yesterday to the moon landing. There's a lot of people out there who feel like America's golden days have passed, so I don't think it would be horribly difficult to link those prosperous times with the moon landing. At the end they could sign off with something like what Aldrin mentioned in his article; “I believe this nation should commit itself, within two decades, to commencing American permanence on the planet Mars.”
The only difference between Kennedy's speech and the Mars speech would be that Kennedy's was used to win the cold war, and the mars speech would be used to fix internal economic strife.