A lot of the guns in circulation in Iraq were liberated from the army and police, or acquired through corrupt channels, originally provided by the coalition forces themselves.
You credit a well armed populace as being the key here, but it doesn't hold up to scrutiny. They could've started with zero guns and simply acquired them as necessary.
Remember, a hostile government might shoot an unarmed individual in a conflict, but they will always shoot an armed one.
This is somewhat similar to another argument I've had - there were some armed Jews in Germany who were able to leverage that firepower to hold off the SS and, eventually, escape. It certainly didn't stop the Nazis from committing the Holocaust, and communication / coordination are key to mounting a successful offense that the Jews didn't necessarily have time to mount, but while there were lots of Jews that died (some of them which might have even been armed), there were some that escaped (some of which were not armed); regardless, guns were demonstrably beneficial to those who fended off the SS.
As pertaining to the US Military, they have proven over and over that guerrilla warfare is not their strong suit, and especially so on foreign soil. Vietnam, Middle East, etc., have all shown that to be true. Also, as was mentioned earlier, many, if not most of the existing armed forces would have a very hard time mounting all out martial law against its citizenry. That isn't meant to imply that the situation couldn't be framed as such that it appeared to be necessary, but that also doesn't hold for long.
You seem to think having piles of guns to start with puts you at an advantage. It doesn't. If anything, having piles of guns is a liability. In Libya they would just raid police stations and military depots and get all the guns they could ever want. I'm sure the same thing is going on in Syria.
Even in a place like Japan where firearms are heavily restricted, it would be only hours after some hypothetical civil war broke out before the resistance was armed.
Guns are an important tool in fighting, but there's billions of them in circulation around the world. If people want guns, they will get them. The amount of initiative lost in not having guns in the first few hours of a struggle is negligible. This kind of unrest takes years to resolve.
On the other hand, a random Israeli has probably participated in mandatory military service even if they don't own a gun.