There are valid questions of what type and level of military force the nation needs for any given period of time based on the perceived level of threat. At the low end of the spectrum, during a time of no perceived lvel of threat, one percent of total population should be available for military service in short order, regardless of composition in service or component. At this level the defense of the Continental U.S. alone can be done with a well trained Guard and Reserve force, supplemented by sufficient blue water naval forces including air and ground assets needed for the protection of the sea and air lines of commerce to the Continent.
At the other end of the scale, such as was achieved during WW2, the nation should be able to go from one percent to ten percent in three years. At this level of involvement, another thirty five or forty percent of the total population would be involved in war production. At the population that means three million in idle times, while serious war would require thirty million. In WW2 we fielded 100 combat divisions (Army and USMC) and 102 aircraft carriers of all sizes. There were twelve million in uniform in WW2 with a population of 120 millions (e.g. 10%)
It is the need to project force overseas, and to deal with extant threats overseas, that standing forces are needed. In between big wars, there is a need for soft power integrated with political, economic, social as well as firepower is needed. Once a big one starts, the need for more firepower and logistics changes the complexion of forces, and both must be planned for, with those forces not needed forward are kept in reserve.
The threat to the Continent should be viewed as how this threat affects the sustainment of the Constitution. The physical attack of the continent or of occupation or destruction of parts of the US must be evaluated in terms of how the government operates in accordance with the Constitution. Washington DC was within the range of the sound of artillery fire for extended periods of time during the Civil War, was burned once by the British neither of which caused the nation to fail.
Both Russia and China lost huge chunks of their territory in WW2 and still functioned as nations. France was occupied during WW2, but was able to keep thier fleet of battleships and cruisers out of the clutches of Hitler, which if he had the French Navy under his control might have given the Germans the upper hand in the Mediteranean, indeed in the whole war at the critical year of 1941.
The Constitution requires three quarters of the states to ratify any changes, leaving one quarter (13) of the states in a position to block any unwanted changes. So long as thirteen states remain independent, the Constitution remains unchanged. The issue of a surrender to foreign forces, the Senate must approve by two thirds any treaty of surrender. Short of that, no surrender would be considered valid.
These numbers assume no secession, and secession is not considered legal at this time, but given the vagaries of chance, this opton would be the biggest threat to the continuity of the nation under the Constitution. It is possible that several states could secede in order to preserve the present form of Constitution which gives rise to an interesting number of scenarios depending on the geographic continuity of the unoccupied portions of the continental USA:
For the sake of simplicity, one could break down the US into six zones:
the Pacific Coast,
the Great Planes,
and the Mountains,
in order of importance. The nation could be still operate with three of these in US control includingone of the first three. It gets to be a problem if there are large non-contiguous areas. The geographic center of gravity is St. Louis which if controlled by a force marching from any direction is in a position to over-whelm the rest.
An prospective enemy thinking about conquering the US, would have to raise sufficient forces and project them onto our soil to overwhelm a military force of thirty million and occupy three of the six areas above. The time to raise such a force, particularly transportation assets would give the US ample time to arrange a warm and permanent greeting for those who dare.
The nuclear option must be considered in the light of those we bombed mercilessly without effect by asking how many cities did the Germans lose before Hitler ate a bullet in his bunker. Allied infantry had to take the streets. Japan surrendered as much as because the Soviet Army was already invading the northern end of the country with the US poised to attack from the south. Hirohito was no Hitler.
Knowing when to quit isn't in any manual for war I know.