You are correct. Anyone who understands the history of facism (and it seems you do), knows it originally grew out of socaist theory. NAZI was just a shorthand term for the National Socialists Party.
Somehow, over the years, this reviled movement has been tied to the right, but it's legacy is truly leftist. Like you, every chance I get I equate Obama to facism, but a lot of historically illiterate people think I'm just being hyberbolic.