With open immigration, the U.S. would become much richer, as it did in the last century. Immigrants would work for less, which would lower the prices of goods and services, benefiting us greatly. Labor is another commodity, like steel or wheat. If free trade is good for the latter two (which it is), it is good for the former.
I’m rather disturbed at the number of people who assume that immigration just makes things worse, without even attempting to provide an explanation. The only person who has even attempted is Merkwurdigliebe, who seems to argue that things are more complicated than Econ 101, without going into much further detail.
Are there negative externalities from immigration? Of course. I don’t think they’re enough to balance out the positive effects, but they exist. The environment is one, although I doubt it’s a major issue. Many people around the world today live without plumbing, clean water, and other things we consider essential. Overall, the environment would probably improve (at least in regard to how it affects humans), since more people would be living in less toxic environments. There might be some job turnover, but that happens with all sorts of changes–it’s the creative destruction critical to economic growth.
The big one is crime–I doubt immigrants are particularly more criminal than natives, but being poorer, they might be. At any rate, even at the same crime rate, natives would disproportionately bear the brunt of incarceration costs since we have higher incomes and thus pay more taxes.
Medical care and schooling are also big issues. While liberals and libertarians would disagree on how to deal with this, the analysis is relatively simple. Libertarians would say that govt should not provide either for immigrants. Liberals would be aghast at this, and demand that the govt provide such benefits. However, it is the liberal position that such benefits have significant positive externalities–society is better off helping out the poor and ill, or educating children. If, say, providing free K-12 education for every person in the U.S. is a good thing, then we should continue to do it no matter how big the population gets due to immigration. Costs may increase at first, but after 1 generation they will be recouped and then some. Voters can decide for themselves which political position they endorse and choose accordingly. Either way, there’s not really a problem.