We've been talking about the second amendment. You have yet to illustrate how the second amendment is vital to and capable of keeping the United States government in check. How does the shotgun in your closet practically and effectively combat the vast militaristic capabilities of the United States?
So first let's begin by laying out what can be accessed legally by U.S. citizens. All manner of machine guns, sub-machine guns, and sniper rifles, including the .50 caliber Barrett (It can punch through tank armor). While automatic weapons aren't allowed, most if not all of these guns can be easily modified to be fully automatic. Military-grade scopes and other accessories can easily be purchased as well. Your ridiculous notion of shotguns vs. the U.S. army is shortsighted and naive. Citizens are able to arm themselves fairly well in this country.
Now that that has been established, let's remember that explosives can also be produced privately and distributed for use. Remember how shaped charges tore apart our M1's in Iraq? The same thing would occur in a conflict over here. Molotov's aren't difficult to make and can take out any unarmored personnel carrier and a whole host of troops. Great, so now the citizenry has explosive tech as well.
Anyways, back to the point. Armed citizens, with the manner of weapons I've laid out, are capable of protecting and defending themselves to a great degree. Most assault rifle rounds can punch through body armor and render vehicles inoperable. Read Black Hawk Down and you'll be shocked to see how much damage these weapons can do, even in the hands of poorly trained Somalis. Armed groups are also capable of raiding U.S. armories, which are not as well protected as one might think, for supplies and weaponry.
The very fact that citizens have at least some way of fighting back is an important point if a country-wide conflict were to break out. Again, the government's vast arsenal is not as important as you would like it to be. The military would not be able to roll up and flatten a city with bombs and artillery to stamp out an uprising, not without incurring the wrath of the rest of the country. America is not the Soviet Union, and plenty of people here don't particularly care for the government as much as you do. The fighting would be up close and personal, and in many cases civilian arms would match military arms. It would be bloody and the army would suffer heavy losses, as nearly every army in history has when fighting this type of battle. As someone mentioned earlier, the citizens wouldn't even need to win any battles to achieve their goals. The VC lost nearly every major engagement they had with us, and yet still prevailed at the end of the war.