I am pretty sure he is referring to the intention of many of the founders for the U.S. to not have a standing army as they were distrustful of them. The intention was to raise an army only in time of war, and allow the unorganized militia to be at the ready if needed for actions less than full scale war, hence the "When called into the actual Service of the United States" portion of that clause. Sometimes, however the needs of reality frustrate the best of intentions, and the fact that we have been in a semi-constant state of conflict over our 234 years just doesn't allow for the military to stand down in the way the framers would have preferred.
Though the argument against the constitutionality of a standing army I believe is fatally flawed, it cannot be fully dismissed as it definitely was the desired position of many of the founding fathers.