Rawls argues that the correct principles of justice are whatever people would choose in the original position (OP). In the original position, parties come together to choose principles of justice which will be used to select the basic institutions of a society they will inhabit. These agents are presumed to be self-interested. They want to pick principles which will improve their own welfare. But they are also imagined to be ignorant of their own particular identities. They don't know whether their relative status or income, their race, ethnicity, and so on. They don't even know the distribution of such identities. Thus, when they choose selfishly, they choose for everyone. And that's what makes the principles good--they're what you would choose for yourself if you don't know who you are. The original position is supposed to force the parties to pick principles (which in turn select institutions) that are good for all.
Except not really.
Some big questions are: Who counts from the standpoint of justice? To whom and from whom are duties of justice owed? Who is part of justice and who is outside justice?
Rawls OP doesn't answer these questions so much as it presupposes answers. When Rawls constructs the OP, he more or less imagines capable, working adults who will live forever in a single nation state. Accordingly, when the OP doesn't generate principles of justice for foreigners, children, animals, or, unborn fetuses, that's not because the theory shows that they are outside justice, or are special cases, or are governed by different principles of justice generated through different means. Rather, it's simply because Rawls designed the OP a particular way. It's arbitrary fiat rather than an insightful or illuminating argument.
If we rewrite the OP to state that the parties could turn out to be, say, unborn fetuses, it would generate very different conclusions. (It would probably end up endorsing a much more pro-life position.) If we rewrite it to say that the parties are choosing principles to select a world order rather than a national order, or that they could turn out to be foreigners and resident aliens, they'd select different principles. If we rewrite it so that they could be animals, we get different principles. After all, the mechanism by which the OP makes the parties pick principles that improve the interests of various groups is that the parties could turn out to be members of those groups. If you make the possible range of identities narrower, the OP selects narrower principles. Make it wider, and the OP selects wider principles.
There is thus not one OP, but many possible OPs. What a Rawlsian-type theory says depends in great part on which OP we think is morally privileged or the "right" OP. Who the parties could turn out to be changes which principles the parties pick and to whom the principles apply.
Rawls's theory ends up being nationalist not because Rawls has an argument for nationalism, but because he assumes nationalism in the design of his theory. His theory ends up endorsing a pro-choice over a pro-life position (I guess; he more or less asserts this in some footnotes but, in typical Rawlsian style, doesn't argue for it) because of what he assumes, not because of what the theory shows.
Similar remarks apply to Rawls's ideas of public reason. If you start by saying that what is legitimate is whatever could form the overlapping consensus of reasonable people in a society, you then have to specify what you mean by reasonable and what counts as a society. Rawls of course famously fudges "reasonable" to exclude brilliant critics like Robert Nozick but to include mealy-mouthed morons like your MSNBC-parroting dad, but he also assumes rather than proves that a society = the adult, human members of a nation-state.