He could, but I am betting he won't. Remember what his brother Jeb said, "The court has ruled and their decision is final."(Terry Schiavo case)
Except of course all the reporting on the story has been completely wrong. All the Court said was Congress, not the President, had the right to set up the Military Tribunals. So while they work the Leftists work into a frenzy, the Republican Congressonal Leadership is preparing a bill. And when that bill comes up the Democrat Congresscritters will have a choice, backstab their froathing Leftist base and defend the country betray the country and piss off the bulk of the American Voters. It's a lose-lose for the Democrats any way it goes.