It's not my belief, DougR. It's what they teach in college level courses that categorize political and economic systems.

Capitalism and socialism are economic systems.

Democracy and totalitarianism are political systems.

Our system, according to the way these things are defined in such college level courses, is categorized as a form of "democratic socialism" because we are a democracy, but we employ some socialistic practices, such as social security and medicare. Our system is partially capitalist, and partially socialist.

Someone please correct me if I'm wrong about this, but my understanding is that there aren't any purely capitalistic countries in the world.

As far as being a republic versus being a democracy is concerned, I don't remember that even coming up. But you could probably substitute the word republic for democracy if you want. So in that case, it would be appropriate to say that the US practices a form of republican socialism. Gee... that has a strangely compelling ring to it ;-)