Otherwise, it's just lip service. Your government is already ignoring your Constitution on a large scale, but apparently nobody gives a damn
I am not American, still, I do truly believe that hundreds of millions of Americans do give a damn.
The problem is not giving a damn. The problem is that guns are a stupid way to try and change governments, and everyone there must intuitively understand this. I keep reading comments by 2nd amendment fundamentalists saying they're packing guns so they can overthrow the government
The first problem is that if you go it alone, if you're a solo shooter, you can't achieve anything and will be killed immediately, then written off as mentally unstable. This does happen in the USA and in at least one case the shooter did claim they were rebelling against the government. Regardless, such events are zero impact.
The second problem is that if you try to team up with like minded people and form a group of armed citizens who are going to engage in a revolutionary coup, you will need to communicate in order to find such people, and at that point you are very likely to attract the attention of law enforcement who have totalitarian surveillance powers and the ability to move against "cults" or "terrorists". And almost by definition if you're trying to overthrow the government through force of arms instead of the ballot box you can be described as a domestic terrorist. You will end up sitting in jail for many years, and most people will likely never hear of you, or if they do read about your case in the papers they will just forget about you.
The third problem is that if you do somehow overcome the first two problems and succeed in forming some kind of revolutionary militia, taking over some territory and defending it against the US army in a new American civil war, you will need a system of government for that territory. How exactly you prevent that new government from eventually going the same way as the existing government would be an open question - attempting to encode the principles of the new state in a constitution apparently doesn't work very well, and I don't see many other ideas from the "guns give us freedom!!" crowd. This is the problem repeatedly encountered by countries in the Middle East where governments are overthrown (without guns, normally) and then tend to get immediately replaced with something worse.
So for these reasons the notion that Americans are free because of guns just doesn't seem to line up with common sense, to me. I cannot imagine any situation in which civil war in the USA would be allowed to happen - civil war is so universally catastrophic that an overwhelming majority of American's would strongly support forcible suppression of an armed uprising using all the tools of a professional army. Your Glock ain't gonna do anything against a Predator drone.