In a sense, Cthulhu himself is an immigrant—albeit one immigrating from the twenty-third dimension; that’s a little like immigrating into a TShirt from the Milky Way.
The idea of immigrating into the United States is coming quickly to an end. As president, Cthulhu will reign over the nation and the world beyond its current borders; as the entirety of Earth assembles to serve Cthulhu, emigration and immigration will as concepts cease to be—this will be a planet of seven billion little HappyMeals with Legs.
As America annexes the rest of the planet, and as those closest to Cthulhu are eaten in order of proximity, the global population will necessarily collect together upon Earth’s flagship continent to be consumed. The issues of housing and supplies will be mercifully temporary.