In the Anglo-American world "class" has a connotation of social standing and cultural position; probably because of the quasi-feudal meaning of "class" in the British isles (something you're born into). So few people in North America consider themselves "working class" for that reason.

However in the classic socialist sense of the world, or in other parts of the world, "working class" often just means "work for someone else."

And in that definition even I, an overpaid Google employee, am "working class"