I must answer that with a definitive yes (and no). There's been examples where technology has "saved the economy" in the past, for example JFK's "put a man on the moon" program, and its incredible technological spin offs, including solid state computer chips.
More recently, we had Ronald Reagan and his "Star Wars" defense programs of the 80's, which pumped computer technology up yet even more, wiring defense department computers together through a network - an internet (originally a DARPA program).
Both of these technological developments (and many more that spun off through these massive government R&D programs) spawned incredible wealth here in the United States. And given the government is about to "invest" trillions of dollars towards improving our economy this year, one might think the time is right to invest in R&D again.
So you asked, "Can technology save the economy?". Given history, I'd have to say it could. However, it appears that our government is spending trillions of "stimulus" dollars in a broad, geographically "even" fashion, "spread around" the entire country. And there doesn't seem to be any real goals, other than to spend of course.
Alternatively, concentrated R&D often focuses in centralized locations, such as Los Alamos, Cape Kennedy, etc. And it has goals.
It still may not be too late to somehow slip in a visionary goal. A 100 MPG, 4 passenger car within 5 years? A 90% efficient solar panel?
Either of these developments would go a long way to reviving our economy. Will they happen, or will our money be spent on a bridge to nowhere?