In the so-called "War on Terror," the whole world may be considered a battlefield, so there is no particular geographic limitation to the killing that the President can demand. Anywhere the supposed "terrorist" can be found is an acceptable place to kill that terrorist, and there really isn't any mechanism for an impartial or third party review, to second guess or otherwise examine that "terrorist" designation. After all, in a war you kill people, and you don't give them a trial first. If we are at war, and the President decides that someone is a terrorist, it's the President's position that the President should be able to have that person killed. Kings used to claim those prerogatives, too, in case you forgot.
If Alexis de Tocqueville were right, this "political question" about the powers of the Presidency should resolve itself into a "judicial question," and our courts should decide the validity of the President's claim that he has the right to order the killing of any person that he, in his sole discretion, decides is a terrorist. How does that Presidential claim hold up against the requirements of the Constitution, which mentions "due process" in quite a few places?
I think that most U.S. citizens would naturally expect that a Presidential claim that the President has the right to decide, based on his own judgment, whom to kill, and whom not to, ought to be subject to some sort of review, somehow. If, for instance, the President decided that my son was a terrorist, and should be killed, I'd like a Judge to review that decision before someone actually carried out the Presidential directive and killed him. You might feel the same about your son. Or your daughter. Or your friend. Or any other person!
Recently, this very case did come to a federal court. And the court proved de Tocqueville wrong. Click right here to read a copy of the Judge's 41-page decision in the case of Nasser Al-Aulaqi v. Leon Panetta. Yes, the former Member of Congress from the Monterey Bay Region was one of the people who carried out those kill orders for the President, and Mr. Al-Aulaqi's son (a United States citizen) was killed. If you would like a shorter summary of the case, you can click on this link for an article published in the Supreme Court of the United States Blog (also called the SCOTUS Blog).
It has long been a policy of the federal courts not to make decisions on "political questions," which are questions which seem to be under the jurisdiction of one of the other branches of our tripartite government. The courts hold that since the President is the Commander in Chief, he and he alone has the right to make determinations like whether or not to kill Mr. Al-Aulaai's son. Or my son. Or yours.
Maybe the Supreme Court will decide it differently, but as for now, the President's asserted right to order the killing of an individual U.S. citizen, if the President decides that he or she has been engaged in terrorist activities, is not an assertion that the courts will review.