Since the best principles of the Constitution include the option of waging war, and since waging war typically involves straight-up killing people, with no other due process than "we think you might be a legitimate target (or at least you might be standing next to a legitimate target)", it's not clear to me what part of the Constitution you think the NDAA is out of line with.
I don't believe it authorizes indefinite detention of anyone, but I do believe it's furthering this recent move to blur the distinction between prisoners of war (not accused of any crime--and subject to the Geneva Convention on the treatment and disposition of POWs--what this law calls "the rules of war") and detainees accused of a crime (and subject to the rights of the accused--habeas corpus, etc.)
If a person is detained as a suspect in the 9/11 attack, then they are accused of a crime. If a person is taken as part of the war in Afghanistan, they are not accused of a crime, but are POWs. It is certainly possible that someone could be in both categories, but that would give them additional protections rather than fewer.
This law seems to say that a person in our custody accused of being involved with the 9/11 attack (a crime) should be treated as a POW. I think that's problematic. The Constitution guarantees certain rights to a person accused of a crime. Boumedienne v. Bush made it clear that holding these detainees by the military and trying them in military courts does not strip them of these rights--not even for non-citizens.
I suspect if the law is used to further the approach that you can strip the rights of the accused if the crimes of the accused are in a class called "terrorism" that the specific workings of that will be reversed, but that there will probably not be a direct review of this section of the law.
I don't think the Constitution "cares" how you define a class of detainees as long as you give anyone accused of a crime the rights of the accused.
I understand there are already procedures whereby people who aren't properly prisoners of war can challenge their detention as that status. (Otherwise, it would make a really big hole in the entire point of habeas corpus rights.)
BTW, from the way I read the Geneva Convention on POWs, if you're taken under the rules of law (and not as someone accused of the crime who gets those rights), you can't be kept in close confinement (prison) at all, but have to be housed the way the military is normally housed. I know it's a bit off topic, but if the argument is that anyone involved in 9/11 is not to be treated as an accused criminal (and afforded the rights of the accused), then they should actually be kept in barracks as POWs.