The logic goes something like this:

I am a patriot, I love my country (or freedom, or liberty, or God, etc).

Therefore, those who are opposed to me are not patriots, and hate freedom, etc.

Since I am a patriot, I must know what is best for my country.

Since they are not, they obviously want only what is evil for my country.

Therefore, as a patriot, I have the moral obligation to stop them.

Since I have that right, I am entitled to do whatever it takes to remove this evil.

Since they are not patriots, no course of action need be ruled out.

Of course, Rush's suggestion is not serious, he's an entertainer, and removing the unifying factor of his audience would be cutting his own throat. But it does serve to energize his listeners and keep their hysteria at a fever pitch. And it does resonate with them to some extent. These are people who see the gun as the solution to all problems; crime, international relations, domestic politics, immigration, high taxes, government regulation, poverty, race relations...

We live in the land of Rocky Raccoon and Travis Bickle.