"[S]everal Republicans announced that they would seek to introduce military detention legislation; it was these detention provisions that ended up in the NDAA."
It's a fairly transparent political gambit. The Republicans attach the military detention provisions to a bill that is political suicide to veto (as it would have cut off funding to the military entirely), and then attempt to hang Obama in public opinion for signing the thing. (Obama, for his part, gave them the opening by justifying detaining terrorists at Guantanamo in an earlier executive order.)
Were I in his position, I'd be setting that part of the NDAA up for constitutional challenges, so that it can be overturned and provide precedence for future court rulings against similar things . . . :
"U.S. District Judge Katherine Forrest in Manhattan ruled that the law, passed as part of the National Defense Authorization Act for 2012, was unconstitutional."