Really? In your scenario the military would also collapse. Obama is already seeking to destroy all US nuclear weapons and all new weapons systems. Who, then, would stop invaders from simply taking America?
"At what point shall we expect the approach of danger? By what means shall we fortify against it? Shall we expect some transatlantic military giant, to step the Ocean, and crush us at a blow? Never! All the armies of Europe, Asia and Africa combined, with all the treasure of the earth (our own excepted) in their military chest; with a Buonaparte for a commander, could not by force, take a drink from the Ohio, or make a track on the Blue Ridge, in a trial of a thousand years. At what point, then, is the approach of danger to be expected? I answer, if it ever reach us it must spring up amongst us. It cannot come from abroad. If destruction be our lot, we must ourselves be its author and finisher. As a nation of freemen, we must live through all time, or die by suicide."
~Abraham Lincoln, Address Before the Young Men's Lyceum of Springfield, Illinois (January 27, 1838)
Seeking to destroy our nukes, yes, but he has not yet had it done.
The military has a tremendous logistical base that is capable of operating without resupplies above the battalion level for a fair amount of time. If the US government were to simply collapse and mobs of civilians roamed the "wasteland" looking for cans of spam, the military would still have huge stockpiles of materials on which to rely for a long time.
Likewise, though the vast majority of civilians in this country are clueless dolts who have a tough time planning dinner, let alone planning how to survive for a couple of days without modern conveniences, there are a lot of us who will weather the storm and thrive.
One of the most immediate threats posed by a collapse of government to the average citizen is brigandage (bandits, roving gangs, whatever). This seems to start immediately prior to and during the break down of law and order, then it just gets worse. Most of them will be armed and, while not necessarily the best or brightest, they do know how to work together to deprive you of what is yours. They understand that there is strength in numbers. These groups generally have a fairly sophisticated logistical base from which to operate, no scruples, and absolutely no qualms about using violence to take what they want. They prey on whomever gets in their way, but they also greedily eye everything that someone else owns. Unfortunately, many of these groups will be military units who have deserted or who are simply desperate for supplies. For a showcase of these bands, take a look at the very real situation in central Africa right now. Anyone who says it cannot happen here is either hysterically blind or just plain stupid.
There is hope, of course. You and I and all of our friends and family who are armed, trained, stocked, and prepared will at least be able to put up a fight in our immediate areas. Bandits don't like getting shot any more that you or I, and they are so fundamentally lazy that, unless really desperate, a goodly show of force will generally convince them to seek elsewhere for victims. Experience is the best teacher.