There are two big things that I think need to be pointed out here. First, you have an assumption that the NSA can crack any cryptographic encryption or hash that they had a hand in developing (SHA-2 being the main example). Can you explain why:

A) Nobody else in the entire world has publicly managed to even come close to breaking SHA256.

B) NIST only recommended that the US Government move from SHA-1 to SHA-2 once it was publicly accepted that SHA-1 was insecure. Now, they're supposed to use SHA-2 everywhere. If the NSA is so far ahead of everyone else, why would they use hash functions they know to be insecure? As soon as a public release of a vulnerability comes out, their security will be severely damaged. (http://csrc.nist.gov/groups/ST/hash/policy.html)

C) SHA-3 was chosen through a contest where researchers publicly submitted and discussed their hash functions. The chosen winner to become SHA-3, Keccak, was selected because it is clearly fast and secure. It was not developed by the NSA, and there would be very little room for the NSA to "rig" the contest, finding a hash function that they, but nobody else, could find a flaw with. Doesn't this show NIST's intent: to provide a national standard for a secure hash, drawn from the minds of the best crypto researchers, in the case of SHA-2 failure?

The other issue I have with this theory is that Bitcoin does NOT use classic DSA. Bitcoin's signatures are done using elliptic curve cryptography. Neither ECC nor ECDSA come from the NSA (Here, here, and here). A vulnerability in classic DSA does not mean there's a vulnerability in ECDSA.

So now we have two cryptographic functions, SHA-256 and ECDSA. SHA-256 is THE standard hash function, which has no public vulnerabilities and there is no evidence I see that would lead me to expect the NSA can reverse it. ECDSA is a fast, secure signature function that uses very different math for its security. The conclusion? Bitcoin was built using some of the most secure cryptography known to man, using multiple functions from different origins and mathematical backgrounds to ensure its security for ages to come. No NSA conspiracy here.