What the Constitution says is 'militia.' That doesn't tell us what militia means. The federal Bill of Rights is based on the Virginia Declaration of Rights, which defined militia as the populace, trained in arms, not a select group of citizen-soldiers. This was also the definition of militia entertained by Madison, as well as the Father of the Bill of Rights himself, George Mason.
A fairly reasonable textualist argument could be made in support of defining the militia as the whole populace, rather than a select group of citizen-soldiers.
Article I, Section 10, Clause 3 declares, "No State shall, without the Consent of the Congress ... keep Troops." What is the difference between a "select group of citizen-soldiers" and "Troops"? Of course, there is no distinction. They are exactly one and the same.
If a militia is only a select group of citizen-soldiers, it would follow that no militia may be maintained without the consent of Congress. However, such a result would contradict Article I, Section 8, Clause 16, which entrusts the government of the militia (when not in the national service) to the states. The clear implication is that militias may be maintained in the first place, without congressional approval. When the Constitution specifically declares that a militia is "necessary to the security of a free State", can anyone claim that a militia's existence is dependent on the consent of Congress?
Thus, if we accept the premise that a militia is a select group of soldiers maintained by the state government, we reach the illogical conclusion that no militia may exist without Congress' permission. Hence, by
reductio ad absurdum, one may establish that a militia is not a select group of soldiers.