The basis of the challenge was that the provisions limiting the ability of persons to file successive habeas petitions violated Article I, Section 9, Clause 2 of the US Constitution, the Suspension Clause.
In addition, the United States Constitution included a similar writ in the Suspension Clause, article 1, section 9: "The privilege of the writ habeas corpus shall not be suspended, unless when in cases of rebellion or invasion, the public safety may require it."
Indeed, there is a respectable argument, based on the original understanding of the Suspension Clause, that the Constitution itself creates no habeas corpus right at all for persons of any type in federal custody and that all such rights are entirely a creature of Congress.
(noting that the Founders "must have felt, with peculiar force, the obligation" imposed by the Suspension Clause).
It was a test of the authority of the President to suspend "the privilege of the writ of habeas corpus" under the Constitution's Suspension Clause.
Petitioners, aliens designated as enemy combatants and detained at Guantanamo Bay, Cuba., have the constitutional privilege of habeas corpus, which cannot be withdrawn except in conformance with the Suspension Clause, Art.
The U.S. Constitution specifically includes the habeas procedure in the Suspension Clause (Clause 2), located in Article One, Section 9.
The Suspension Clause of Article I does not expressly establish a right to the writ of habeas corpus; rather, it prevents the U.S. Congress from restricting it.
The opinion explicitly stated that, because DTA did not bar it from considering the petition, it was unnecessary to decide whether laws unconditionally barring habeas corpus petitions would unconstitutionally violate the Suspension Clause.
Regarding the application of the Suspension Clause of the Constitution, Scalia points to Johnson v. Eisentrager.