Sorta interesting website,
http://www.numbersusa.com/overpopulation/immtrad.html. The rhetoric reminds me of the conservatives' strawman liberal rant, phrases like "Robber Barons of the Guilded Age more than tripled the level of immigration, using it to keep wages for all American workers low, to bust unions and to keep freed slaves from moving off the South's plantations to take jobs in the North" and "major industries were addicted to cheap foreign labor that enabled them to keep wages down for all Americans." I think Marx would be proud that his rhetoric lives on.
In any case, it doesn't make a real case for limiting immigration and for the most part distorts immigrant rates through US history.
While no longer true because of high population growth outside the US, Schumaker noted in "small is beautiful" that the entire world's population could be moved to the US and the US population density would still be lower than in England at that point in decline from being the world's sole superpower, and in population numbers. And even China with a population density four times that of the US has vast tracts of undeveloped land, greater in size than in the US; remember the land areas of the US and China are the same.