Let's see what James Madison, the gentleman who was the primary author of the Bill of Rights had to say on the subject:
"The only refuge left for those who prophesy the downfall of the State governments is the visionary supposition that the federal government may previously accumulate a military force for the projects of ambition. ... [Here Madison describes a chain of events, unlikely as he thought them, that might lead to such a force being gathered] ... Let a regular army, fully equal to the resources of the country, be formed; and it would not be going too far to say that the State governments, with the people on their side, would be able to repel the danger. The highest number to which, according to my best computation, a standing army can be carried in any country, does not exceed one hundredth part of the whole number of souls; or one twenty-fifth part of the number able to bear arms. This proportion would not yield, in the United States, an army of more than twenty-five or thirty thousand men. 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." James Madison, The Federalist Papers 46.
This was one of the arguments given for accepting the Constitution with its much stronger central government (compared to the Articles of Confederation). An army about three times the size relative to total population, as the US army is today, would be overwhelmed by a citizen militia of a number amounting to essentially every free male (an issue at that time) capable of bearing arms.
Note that the 1790 Census listed a total population of "free white males 16 and over" of just over 800 thousand. Since some folk would be too old, or infirm, or otherwise not able to serve in the "militia" this is another confirmation that Madison's "militia" was the entire population of the US capable of bearing arms. And here we see from his own words that one of the purposes of that militia was to serve as a check against the possibility of the Federal government using a standing army against the rights of the States and the People.
And since Madison was the primary author of the Bill of Rights, I think this should put to rest any further speculation about what "a well-regulated militia, being necessary to the security of a free state, the right of the people, to keep and bear arms, shall not be infringed." A good part of "security of a free state" is security as a free state. And the very purpose is to ensure that the States had sufficient strength, militarily, residing in their "militias", which was to say the whole of their people capable of bearing arms, to outweigh any attempt by the Federal government to overpower the States.
One thing to consider is that a "well-regulated militia" must, of course, be "well regulated" according to the meaning of those who wrote the Bill of Rights and whether the National Guard serves that purpose today. But what did "Well-regulated mean? Contrary to popular modern belief it did not mean "under government control. Consider the usage examples from history of the term (taken from the Oxford English Dictionary):
1709: "If a liberal Education has formed in us well-regulated Appetites and worthy Inclinations."
1714: "The practice of all well-regulated courts of justice in the world."
1812: "The equation of time ... is the adjustment of the difference of time as shown by a well-regulated clock and a true sun dial."
1848: "A remissness for which I am sure every well-regulated person will blame the Mayor."
1862: "It appeared to her well-regulated mind, like a clandestine proceeding."
1894: "The newspaper, a never wanting adjunct to every well-regulated American embryo city."
Here we are. "Well regulated" does not mean "under government control" but rather something along the line of "in good working order" or "doing what it should."
Well, one of the "what it should" for the militia is to serve as a check against Federal power. Can the National guard serve that purpose? The National Guard is 1) smaller than the national military, 2) often less well armed (many guard units, in my experience, have been armed with obsolete "castoffs" of the regular military), 3) paid for by the Federal government 4) subject to call-up by the Federal government at any time with the State having no authority to overrule that call-up, 4) provided with such arms as it has by the Federal government and on and on and on. A lesser armed force can stand against the Federal government if it is numerically superior and has local support (see Vietnam, Iraq, and Afghanistan for examples). However a force that's smaller, less well armed, and relies on the Federal government for pay and equipment cannot serve as a check against Federal power. It's a part of Federal power regardless of it's on paper attachment to an individual State. Thus, the National Guard, by definition, cannot be the "well regulated militia" that Madison describes in the Federalist papers. It does not meet the "well regulated" part (as Madison understood the word to mean) because it could not stand as a check against Federal power over the States.
The "well-regulated militia" remains today what it was to Madison--the whole of the people capable of bearing arms.