I'm pretty sure this could be solved by executive order, and/or the DOJ filing with the petitioning the SCOTUS to rule it unconstitutional.
IIRC, the Guantanamo terrorist prison program was also created without congressional action, yet its closure was successfully prevented by Congress -- or at least, congressional opposition to closing it was sufficient for Obama to escape blame for failing to close it as he had promised during the election.
So, this could just be a plan to transfer blame for the NSA onto Congress. If he proposes a bill to reign in the NSA that he knows Congress will not pass, it maintains the status quo but he can say that he wanted to end it.
He sends legislation to congress to "fix" the problem and it never gets through. The whole thing is a smoke screen.