IMHO the "we're the best" chants carry a very strong element of truth. The US is still a beacon for the enthusiastic and the innovative. It still offers creators the biggest chance to get funded and be rich. Unless that goes away, the US is still going to be the one to beat economically.
What they have lost is the ability to lead by example- something that has carved a hold in the US psyche even if they can't actually put their finger on it. Being "the good guys" in the eyes of fellow men has been important to the US since the very start.
IMHO the current problems will be overcome because the US people have such strong belief in themselves and their institutions. Then they'll overcome their trade deficit, and then while they're on a roll they'll create an enormous new frontier to stimulate industry and propel themselves into another cycle of growth and leadership. It'll be something really big to enthuse and impress the whole world.
"... They ne'er cared for us
yet: suffer us to famish, and their store-houses
crammed with grain; make edicts for usury, to
support usurers; repeal daily any wholesome act
established against the rich, and provide more
piercing statutes daily, to chain up and restrain
the poor. If the wars eat us not up, they will; and
there's all the love they bear us."
-- Shakespeare: Coriolanus, Act 1, scene 1