Perhaps I just don't understand the terminology here, but which large countries are not considered nation-states?

I think the OP used the term nation state when he meant sovereign state; it was just a mistake of language. johnlepson, on the other hand, seems to have a bee in his bonnet about the US not being a nation state. Whether the US is a nation state or not depends on how multicultural you think it is; it's a political disagreement.