Yes!!! Those who arrived on the Mayflower weren't immigrants!
[Huntington] points out, for instance, that the U.S. is not “a nation of immigrants.” It is a nation that was founded by settlers—who are very different from immigrants in that they establish a new polity rather than arrive in an existing one—and that has been occupied since by the descendants of those settlers and of immigrants who came later but who assimilated into the American nation. Americans therefore are under no moral obligation to accept anyone who wishes to immigrate on the spurious grounds that everyone is essentially an immigrant. Americans own America, so to speak, and may admit or refuse entry to outsiders on whatever grounds they think fit.
[emphasis added]It might be worthwhile to go house-to-house across the land to get the ideas in that paragraph into every citizen's head.