In a post called Arizona Demographics Irreversible...If" I mentioned several kinds of enforcement that could prevent the "irreversible" Hispanic takeover of Arizona. Peter Brimelow reminded me that I only mentioned things that affect illegal immigration. It's also true that a lot of this "irreversible" stuff wouldn't be so if there were a moratorium on legal immigration.
Remember, the United States actually had a de facto moratorium between 1924 and 1965, and it did lead to assimilation.
It didn't lead to much change in voting patterns, though. Steve King of Indiana said once that people who didn't believe this should "go look for an Irish Roman Catholic Republican in Boston."