This is not and never has been unconstitutional. It's NOT unconstitutional to deny Habeus Corpus to either Legal or Illegal Enemy Combatants. As a matter of fact, it's good that the Congress is finally feeling it's oats with regard to reining in the Courts who keep grabbing more and more power to themselves. This is exactly what the Constitution calls for to redress power grabs by one of the three branches.
(e)(1) No court, justice, or judge shall have jurisdiction to hear or consider an application for a writ of habeas corpus filed by or on behalf of an alien detained by the United States who has been determined by the United States to have been properly detained as an enemy combatant or is awaiting such determination.
Congress is specifically prohibited from suspending the Writ of Habeas Corpus, except in cases of Rebellion or Invasion, by Article I, Section 9 of the Constitution.
The last paragraph, in blue, negates the ones in bold and italics. It is that simple. All it awaits is a court challenge. There has been no declaration of Rebellion or Invasion. Therefore, the act is invalid. One cannot legislate constitutionality. It is, or isn't.