Fox News, mainly, just exploits a mind-set which existed long before Fox News was around. It certainly does do propaganda effectively, but its effects are limited to those who are predisposed to see things their way in the first place.
I think that some of us don't understand that when they say things like "liberal" or "left-wing," they aren't using those terms to mean the same thing that we mean. For them, these terms mean "the Others" or "the Dangerous" not "liberating" or "progressive." So they can say that Westboro Baptist Church is left-wing and really understand that to be the case. There's no sense of irony or double-talk.
I know this is the case because I belong to a public-speaking club that had several Tea Partiers in it. I heard them (mis)using terms like "liberal" so often that one day, when I was in charge of the impromptu-speaking portion of our meeting, I showed them the dictionary definition of the word "liberal" and then asked them to speak about the concept using the term that way. Not only could the Tea Partiers not do so, try as they might, they also disbelieved that the term was defined that way in the dictionary.
It's one of the things that's so strange about public discourse in America. We're speaking past each other, in part, because we aren't even using the same language as each other, even though it may sound like it.