In argument Wednesday, three of the court's four conservative members -- Chief Justice John Roberts and Justices Antonin Scalia and Samuel Alito -- expressed skepticism from the bench that foreign enemy combatants at Guantanamo have such a right either under common law or the Constitution.
Common law is derived from court precedents.
The fourth member of the conservative bloc, Justice Clarence Thomas, followed his customary practice of not commenting from the bench.
The ninth member of the court, Kennedy, may provide the deciding vote in a 5-4 decision.
Kennedy was part of the 6-3 majority in 2004's Rasul vs. Bush in which the high court decided, on statutory grounds alone, that foreign Guantanamo detainees had the right to access the courts.
Justice Sandra Day O'Connor was part of that 6-3 majority, but she has retired and has been replaced by Alito.
Rasul was reversed by Congress in the 2006 Military Commissions Act, which denied foreign detainees habeas corpus and gave jurisdiction to military commissions at Guantanamo.