George Borjas is one of the most prominent anti-immigration economists and his research is normally cited by the anti side. The standard line is that immigrants have depressed the wages of low skilled Americans by 8%. I not bothered by this figure in the least and some of the most vigorously pro-immigration economists have accepted that figure (Bryan Caplan uses the figure here). Turns out that it's an oversimplification. This post contains a table with more data about the effects of immigration. 8% is the figure for the short run effects on high school dropouts. The long run effects on high school dropouts is 4%. Other skill groups do better; in fact high school graduates who don't go onto university actually gain.
Remember these are the pessimistic figures.
A while back Paul Krugman wrote an article which was fairly negative about immigration, it included this quote:
First, the net benefits to the U.S. economy from immigration, aside from the large gains to the immigrants themselves, are small. Realistic estimates suggest that immigration since 1980 has raised the total income of native-born Americans by no more than a fraction of 1 percent.Bryan Caplan responds
Horrors! Only a small gain to native-born Americans? Something's got to be done to fight this small gain.You see why he was such a hero?