I think this is pretty rosy-colored view of what would happen. A "large minority" would have to be several hundred thousand people, perhaps a few million. Anything less is just a radical cult that will promptly be put down...and everyone will say "thank goodness" as they watch on the evening news. If something big enough happens that a few million people take up arms, you have a full blown civil war and things are totally different.
Stockpiling guns and weapons is the opiate of libertarians - "it's fine, I have the weaponry I need to overthrow the government if things get bad enough". In reality, you have a better chance fighting zombies than successfully overthrowing the government through violent means.
To be clear, I have nothing against guns. I'll probably purchase one once I've moved into a more rural area. But I'm under no illusion that the weapon will ever be useful in deposing any government.