the NDAA killed the first, fourth, and sixth amendments.
The NDAA provision is a statutory law, it CANNOT overrule any amendment. If they are in conflict, then the NDAA loses.
And after that, WTF? How did it kill the first amendment? Did it establish a relgion? Prohibit the free exercise of religion? Abridge the freedom of speech, or press? Or our right to peacefully assemble? Or did it eliminate our ability to petition the government for a redress of our grievances?
Actually yes, a strong case has been made for how NDAA abridges freedom of speech for the press: http://www.alternet.org/story/153843/chris_hedges%3A_why_i'm_suing_barack_obama/