It's the end of the world as we know it (and I feel fine)
blog.cryptographyengineering.com
blog.cryptographyengineering.com
If they did, how would we know?
During WWII, after the Allies had broken the Enigma cipher and were reading all the German communication, they still had to allow enemy actions that would result in loss of human life, just so they wouldn't tip their hand and reveal that they had broken the code.
I'd assume it would be the same today - a plausible non-crypto way of getting data came out ("We beat him with a pipe until he told us the password", ala http://xkcd.com/538/ ) would be a better explanation than if they broke a code with some quantum ubercomputer.
The Enigma case doesn't really apply here - the US was not using the known flawed encryption themselves, and tipping the public off by calling for the development of a new standard only means that AES might be broken in the next decade or two, and maybe not by quantum computers. Cryptographers already recommend switching from weak algorithms years before they're fully broken.
RSA and other key exchange techniques are another story though, as the article mentions RSA is theoretically significantly weaker to a functioning quantum computer than AES to start with, and I don't really know the extent to which the government uses RSA.
NSA Suite B Cryptography recommends use of ECDSA over RSA, but the latter is acceptable for documents with "SECRET" classification level.
Forgive my ignorance of quantum computing, but the classical computer can see the future in a finite image space by computing every image combination. It just turns out to be a lot of computing to see every variation in any space of reasonable size.
Isn't this something a quantum computer would excel at, by computing the variations concurrently?