Most countries in the Middle East have mandatory military service. If they get invaded by a foreign force, they can raise local militias very quickly from people who not only already own guns, but also have received significant training in their usage and can get organized quickly due to the time they spent in military.
In contrast, most Americans don't know how to hold a gun, much less fire one. And even those who are serious about guns have not actually been part of any military, or even a militia. Frankly, they would get mowed down by any sort of organized force in very quick order.
There are 11.6 million veterans below the age of 65, which is a fair amount of trained soldiers, though that doesn't say anything about sides.
Also, merely counting guns per capita tells you very little as some people have lots of guns. You have ~ 40% of households with a gun and ~ 70% of people between the ages of 15 and 64.
This translates to ~ 80 million people of military age with access to firearms, and assuming that most veterans are in the households that have guns, up to an eighth of them trained to a high standard.
Now this, if it rose up and could be commanded as a single force, would be the largest military in the world, in terms of forces. However the only circumstance that I could see that even partially happening would be in response to an external military invasion.
What is far more likely a scenario if the US becomes unstable is a complicated civil war started by a state attempting to secede, the federal government reacting, then more states getting involved. In that case you never get one big force, just lots of smaller state forces with the military not wanting to get involved at all, but at most trying to act in a peacekeeping role and making sure that the big guns stay locked up.
One thing to keep an eye out for, as I have said elsewhere, is that the military equipment given out is partly going to pro-secessionists in local and state police forces and it may be worth considering that the police in Missouri may not be merely incompetent in the way they are currently reacting to events.
I am from the UK, and the fact that lines like, "You have ~ 40% of households with a gun and ~ 70% of people between the ages of 15 and 64" are bandied round so readily is completely terrifying.
Have you thought about why you have this irrational fear or does the fact that it's commonly shared among your society lead you to believe its not irrational?
Most countries in the Middle East have mandatory military service. If they get invaded by a foreign force, they can raise local militias very quickly from people who not only already own guns, but also have received significant training in their usage and can get organized quickly due to the time they spent in military.
In contrast, most Americans don't know how to hold a gun, much less fire one. And even those who are serious about guns have not actually been part of any military, or even a militia. Frankly, they would get mowed down by any sort of organized force in very quick order.