Sloppy use of language does not help the discussion. If your friend has been drinking and insists on repeating this meaningless phrase we are a nation of immigrants over and over like a mantra, explain to him that if he is, for some inexplicable reason, including ancestry in his argument, then all nations are nations of immigrants and we should simply open the borders. If he has been drinking a lot and this sounds like a good idea to him, take his keys away and suggest he go live for a while in a Third World country, asking himself why everyone there is coming here. Since this is a democracy, let's put it to a vote. We will win that vote.
Every sovereign nation has the right and obligation to protect itself.
Because we are a nation of immigrants, we have to allow for massive immigration which, in turn, makes us a nation of immigrants. Hence its circularity. Circular arguments are invalid in the logical sense by virtue of HOW they are structured and not WHAT do they mean.