Let's just establish the framework that Publius is working within:
This decision of the scope of review is dependent on the structure of the constitution and where it vests powers. Just a couple examples:
The Constitution vests regulation in Congress. The Court's role is not to decide how it would regulate, but to decide how Congress did regulate. Assuming that Congress isn't violating other parts of the Constitution, it should, then, pull all the meaning for "The Law" from the statute, not itself. Complete deference to Congress when acting within its powers. (Tribe, American Constitutional Law)
When Congress vests some of this power in an agency, the role of the Court is not to provide the meaning, but to make sure that the Agency is acting within the scope of its delegated authority, within its powers as vested. Complete deference within that scope. (Chevron; Monaghan, Marbury and Admin State)
The political question doctrine is merely a determination that the question asked is one that the Constitution directs the President to answer. The Court determines only that this is, in fact, a question for the President, and if it is, complete deference. (Henkin, Is there a Political Question) [emphasis added]
Further, he thinks that we can draw a line between what is permissible for citizens and non-citizens:
I don't have the answer, only (I think) the question. My guess is that the regulation of prisons full of POW's and terrorists is something that is very tied to the Commander in Chief power, and something that the Courts, and the legislature for that matter, should not be in the business of regulating. Youngstown constrains these powers in their use against citizens, but I think POWs, and especially non-state terrorists should fall outside Youngstown's holding.
Now, what about me? I think that when it comes to matters purely contained to fighting wars, the president has considerable discretion (there are some areas in which congress can legitimately intervene, but they are not material to our discussion here). However, like with congress, this privilege only extends as far as the president not violating other parts of the constitution. Hence, if the president, in the course of his war-fighting acts, violates a constitutional right, then the court's can legitimately restrain the action (just as when congress, when passing a law that otherwise would be legitimate under Article I.8 violates the constitution, we can strike that down too). This is pretty well established (see, e.g., Ex Parte Milligan 71 U.S. 2, (1866) (the President must, if possible try civilians in civilian courts even during war) U.S. v. U.S. District Court 407 U.S. 297 (1972) (national security, by itself does not eliminate 4th amendment safeguards), Youngstown)
Publius seems to concede as much when he admits that unlimited presidential actions against civilians is likely uncosntitutional. The question then becomes how, if at all, the rights of aliens and non-citizens differ from those of citizens.
At the outset, we must acknowledge that aliens must possess some rights under American constitutional law. Presumambly the government could not decide to summarily execute our entire immigrant population on a whim. This is not something that requires us to go beyond the text of the constitution. The 4th, 5th, and 14th amendment by their terms apply to all persons within the jurisdiction of the United States, not just citizens (the 6th amendment refers to "the accused," which presumably can include non-citizens as well). As Justice Brennan observed in Plyer v. Doe
"Whatever his status under the immigration laws, an alien is surely a "person" in any ordinary sense of that term. Aliens, even aliens whose presence in this country is unlawful, have long been recognized as "persons" guaranteed due process of law by the Fifth and Fourteenth Amendments...Indeed, we have clearly held that the Fifth Amendment protects aliens whose presence in this country is unlawful from invidious discrimination by the Federal Government" [457 U.S. 202, 211 (1972) (internal citations omitted)]
Therefore, it seems abundantly clear that, with reference to the rights in question, aliens have a just claim to them that is reviewable by the courts.
Hence, under the constitution, the president does not have unlimited rights as what to do with persons caught and charged with a crime (in the case of so-called "enemy combatants," war crimes). Either he has to label them POWs and treat them as such, or try them in accordance with the laws of the nation as the constitution requires.