Can the President order an assassination in the United States? The administration thinks that he can. I don't. Here is a common counter-example that I'll use to explore what I mean when I say that (largely reprinted from a comment I made at Talk Left).
"Did they not already do this when Cheney ordered that a hijaked airplane be shot down over PA? It would have killed not only the hijackers but all the passengers as well."
The hijaked airplane was en route to crashing into a building and killing more people, who would die anyway if no action was taken. Bringing down that plane would have been just as lawful, under general principles of criminal law, if a private citizen, overhearing radio traffic, understood what was going on, rammed his own private plane into the hijacked aircraft causing it to crash and somehow escaped alive.
The use of deadly force in true self-defense (and the related defense of others) from an unavoidable deadly threat actually in progress is uncontroversial, particularly in a case like that where the choice of evils (everybody on the plane dies, or everybody on the plane and everybody on the ground where it hits dies) is clear.
But, FBI directors, judges, mayors and sheriffs almost never give orders to kill somebody within the U.S. The lawful and usual order is to use the force necessary to arrest a dangerous person, either someone who has committed a crime or someone who is attempting to commit a crime (which is itself a crime). Deadly force might be justified in making that arrest if necessary to prevent imminent harm to the person making the arrest or others, in the immediate circumstance, but this isn't something that is lawfully ordered up front.
But, this is war, you say. The AUMF (authorization of use of military force [against Al-Queda passed shortly after 9-11]) makes it legal. Not so fast. The AUMF authorizes necessary force. It is very, very hard to imagine any scenario where an assassination ordered by the President in advance is necessary in a place where the courts are functioning in the United States, in circumstances which would not be lawful in the absence of a Presidential order.
Does the President assert the right to, for example, assassinate someone acquitted of terrorist conduct in a court of law, because he thinks he know that the person is guilty and will commit another terrorist act, because the legal system is unavailable for vindicating the past offense? Could the President order the assassination of one of a proposed terrorists three innocent infant children to show that he is serious and will kill the others if the alleged terrorist doesn't comply? Do we want to not only negotiate with terrorists but negotiate like terrorists? You can spin hypotheticals all you want, I don't think that there is ever a legitimate siutation when it is necessary for a Presidential assassination of a terrorist suspect (which is all that has been claimed so far) ordered in advance on U.S. soil.
The United States (and indeed, most of the civilized world) is not currently a battlefield, no matter how paranoid national security official might get. It was, in certain places, during the Civil War, it isn't now. Orders to kill are made by military offiers, against well defined enemies, in places where killing is necessary because there is insufficient law and order to try and arrest someone. Obviously, it is impossible for Marines to arrest German soldiers in a pillbox with a machine gun atop the cliffs of Normandy. Obviously, arrests can turn bad when the subject of the arrest pulls a gun and prepares to fire back, instead of surrendering. Obviously sailors in one boat can't arrest the soldiers in another boat that is firing upon them (or that they know would fire upon them if it knew they were there). But, these necessities either can be foreseen in advance as certain to happen, or don't come up at all, in places where law and order prevail and the courts are functioning.