It was in the debates.
From Federalist #29:
it will be possible to have an excellent body of well-trained militia, ready to take the field whenever the defense of the State shall require it. This will not only lessen the call for military establishments, but if circumstances should at any time oblige the government to form an army of any magnitude that army can never be formidable to the liberties of the people while there is a large body of citizens, little, if at all, inferior to them in discipline and the use of arms, who stand ready to defend their own rights and those of their fellow-citizens."[L]ittle, if at all, inferior to them in discipline and the use of arms" means that the people were expected to have the same arms as the army, and be just as good at using them.
-PJ
Yeah, I need some range time.