I'm no white supremacist, but AFAIK "Government nigger" isn't some kind of common insult, or even a catchy insult. I'm more inclined to believe he just fluffed his line, he meant to say something like Obama is a "anti-war peacenik" or "anti-government peacenik" but ended up as "anti-war government nigg...".
Based on my own experiences, when you are making a speech without a script (e.g. going into a meeting impressing clients), you just remember key concepts you want to drive home and then make the sentences off the top of your head. The more nervous you are, the more likely you will fluff your line. I think that was what happened with
Rick "where the sun don't shine" Santorum.