The same discussion list that prompted Ilya's post raised the question whether the Coast Guard is constitutional. The answer to that strikes me as simple — the Coast Guard is a naval force, and as such is well within Congress's power to "provide and maintain a Navy." That Congress may choose to break the Navy down into two departments under two different heads is not, I think, a problem: Both of them, put together, would constitute the constitutionally sanctioned Navy.

The tougher conceptual question is whether the Marines can constitutionally be considered part of the constitutionally specified Navy (whether or not they are part of a federal agency labeled the Navy), or must be seen as falling under the constitutional head of "Armies." In either event they'd be constitutional, but if they are treated under the head of "Armies," then they'd have to be funded using appropriations that are for no longer than two years; if they are treated under the head of "Navy," they can be funded under unlimited-length appropriations. Recall that the relevant Congressional powers are:

To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;

To provide and maintain a Navy.

I don't know the answer, but I thought I'd flag the question (recognizing that it is of little practical importance, especially these days).

UPDATE: Some comments point out the long history of the Marines as a branch of the Navy, stemming from the Marines' having historically been sea-borne troops.

Nonetheless, the reason for my question is that today (as I understand it), the Marines often operate well away from all coasts, and are functionally a land fighting force.

My (somewhat vague) recollection is that the constitutional distinction between armies and the navy stems from the fact that Englishmen of the time -- including the American variety -- saw land-based forces as much more dangerous to domestic liberty than sea-based forces, and sea-based forces as much more important to day-to-day national defense. That's also why there was lots of concern about a standing army, but not about a standing navy. Modern Marines are in this respect at least potentially more like "armies" than like the "navy"; that's why the question I pose is theoretically nontrivial.