Expanding on my earlier answer, Susanann, I don’t see any circumstances in which private gun ownership - wedded to the idea though you are - gets to be a factor to any useful extent. For the question to be relevant in the first place we have to assume a sizeable Nazi armed force arriving in the USA, which is hard enough to wish up even as a thought-experiment. Perhaps we can assume the Amerika bomber becomes a viable proposition, the Amis don’t get the Bomb and the Nazis do, and they successfully force the States to sue for peace and stand down its armed forces.
Once the Nazis arrive in force, we can be sure that eliminating private gun ownership is high on their list of concerns. The point is that this is by no means unachievable. The French made the mistake in 1940 of trying to fight the War of 1914 all over again; it would be foolish to assume that American elements, absent their conventional armed forces, would be able to fight the War of 1776 all over again.
American revolutionaries were blessed with firearms at least the equal of anything the British could bring against them, and were able to profit from tactics that weren’t up to prosecuting the mother country’s aims. Translate it to the mid 1940s though and the picture changes thoroughly. The best handguns available to the American private gun owner, with the occasional rifle and even more occasional Chicago piano, don’t stack up against professional riflemen with plenty of full-calibre machine-guns, heavy weapons support, and ample experience of front-line combat.
It’s been emphasised elsewhere on these boards that privately-held guns, even in the hands of enthusiasts with plenty of target practise, are by no means a given for personal defence against even an armed criminal: The amateur marksman, unused to shooting for blood, sees his accuracy go through the floor. How much the worse when the amateur must slug it out with battle-hardened troops. And this assumes that the Wehrmacht will be obliging enough to blunder into small-arms range. If they’re smart, they let the artillery do the talking from five miles away, or the machineguns from six hundred yards.
Having a hundred million privately held guns is all well and good if you can count on a hundred million wielders being willing to sell their lives one at a time. One brave Ami with a gun taking one Nazi at the cost of his own life represents an unsustainable rate of attrition for the occupying force if it‘s repeated a millionfold. But grant the occupiers enough sense to use a carrot and stick approach: A tolerable occupation with reasonable freedom and privileges for those who toe the line, and perhaps a partition of the country after the manner of France. In the Occupied Zone, the Germans enforce martial law. Elsewhere - perhaps south of the Mason-Dixon line - there is a friendly American government. That leaves the Americans with a lot to lose if they cut up rough. Meanwhile, the occupiers come down hard, with overwhelming military force, on any pockets of resistance. They are no strangers to enforcing vicious reprisals.
Given the right approach, the Amis might be able to make the States ungovernable; but to make a Stalingrad of every city in America would require a willingness on the part of the people to suffer Stalingrad-type hardship. The question is whether the will would be there.
For my money it was Uncle Sam’s immense logistical superiority, the ability to feed, arm and supply a large armed force from a massive impregnable industrial base, and the sheer unbridgeability of the Atlantic and Pacific Oceans, that made invading the States utterly unviable. Private gun ownership didn’t register as a blip on the scale.