Federalist No. 46: Madison's brilliance
In Federalist No. 46, Madison calculates (quite accurately, BTW) that the new government could support a standing army of no more than 25,000 men, and
To these would be opposed a militia amounting to near half a million of citizens with arms in their hands, officered by men chosen from among themselves, fighting for their common liberties, and united and conducted by governments possessing their affections and confidence. It may well be doubted, whether a militia thus circumstanced could ever be conquered by such a proportion of regular troops. . . . Besides the advantage of being armed, which the Americans possess over the people of almost every other nation, the existence of subordinate governments, to which the people are attached, and by which the militia officers are appointed, forms a barrier against the enterprises of ambition, more insurmountable than any which a simple government of any form can admit of. Notwithstanding the military establishments in the several kingdoms of Europe, which are carried as far as the public resources will bear, the governments are afraid to trust the people with arms.
A useful quote, of course. But look at the brilliance of Madison's strategy....
The debate had, until then, been standing army vs. militia, and the federalists were getting the worst of it. The Constitution allowed Congress to form an army with no limitations save that it had to be funded no more than two years at a time (a carryover from British law) and Americans were seriously worried about a standing army (which might just take over the country, or be used by the national government to do so) and strongly supportive of defense by militia instead.
Federalist 46 deals with the issue in imaginative and brilliant form. Madison argues that standing army vs. militia is a false dichotomy. The nation can have both, and it is precisely the militia that makes the standing army a safe thing to have. Let Congress form the largest army it can possibly create, and it would still be greatly outnumbered by armed citizens answering to State-appointed officers. Madison thus neutralizes a key antifederalist argument, and demonstrates that the Army clause of the Constitution is no danger to freedom.
This of course doesn't do much for the "National Guard = militia" claim. With the dual enlistment requirement, Guardsmen must enlist in the regular Army (or other branch) Reserves. When he calls them to duty, the President doesn't use the constitutional power to call out the militia (I'm not even sure the statute implementing that power is still on the books), but legislation enacted pursuant to the Army clause.