Neoperiapt currently has a very good article posted up about Abu Gonzales and his statements that the writ of habeus corpus is not a constitutional guarantee. Neoperiapt cites a fairly old case, Ex Parte Bollinger, which says that Art. I, s.9, c.2 of the U.S. Constitution does not actually guarantee the existence of a writ of Habeus Corpus. Given that this decision was authored by Justice Marshall, it is entitled to great deference in my opinion. (This is the same Justice Marshall who decided Marbury v. Madison - yeah, THAT Justice Marshall.)
But, there is a case of more recent vintage, INS v. St. Cyr, 533 US 289 (2001). In St. Cyr, a 5-4 decision, Justice Stevens wrote in the majority opinion that "at the absolute minimum, the Suspension Clause [Art. I, s.9, c.2] protects the writ 'as it existed in 1789'" (citing Felker v. Turpin, 518 US 651 (1996).
You can already guess who the dissenting Justices were, right? Luckily, O'Connor was one of the dissenting Justices, so "Strip Search" Sammy Alito can't swing the vote. And Roberts may even swing the other way (hey, I can dream right?).
Thus the most recent case on point says that at the very least, the Suspension Clause says that Habeus cannot be rolled back to pre-1789 protections. (By the way, the 1789 version of Habeus isn't that great, but it does beat no Habeus.) At best then, for now, the Congress can tinker with the exact mechanics of habeus, but cannot eliminate it all together. Thus, the Court through Justice Steven's decision has limited the effects of the venerable Bollinger decision with respect to using that decision to affect an elimination of habeus altogether.