Besides the fact that Abdulmutallab provided "useable, actionable intelligence” upon initial interrogation, which occurred at the hands of FBI agents without reading him Miranda rights and without having a lawyer present, Giuliani is simply wrong about the notion and utility of naming someone an enemy combatant. As the inimitable Mike Isikoff asserts below, we actually haven't named anyone arrested in America an enemy combatant since June of 2003.
Since then both the Bush and Obama administration have detained and prosecuted terrorists arrested in American using the U.S. criminal justice system. This has resulted in the successful prosecution of several hundred terrorists. Using Giuliani's preferred enemy combatant, military tribunal system found at Guantanamo Bay? We have only had three successful prosecutions since 9/11. But Giuliani prefers beating his chest to actually bringing terrorists to justice.