I've seen some conservatives characterize the most recent Congressional Budget Office report on the Gang of 8 immigration bill as saying that the bill will reduce Americans' wages.
It does not, in fact, say that. As they write, the wage numbers "represent differences between the averages for all U.S. residents under the legislation—including both the people who would be residents under current law and the additional people who would come to the country under the legislation—and the averages under current law for people who would be residents in the absence of the legislation." In other words, if you start with 10 middle-class Americans and then add a poorly educated Mexican immigrant into the mix, the average wage of the group can go down even if each individual person's wages go up. It's the shifting of the low-income Mexican person into the comparison set that drives the average down, not a decline in anyone's living standards.
The larger point, though, is about timing. The way the CBO thinks about this is that an influx of new people has the result of leaving the country with fewer capital goods per person. The reduction in the per capita stock of capital goods per person temporarily reduces wages and increases investment. Then, over time you end up with a larger stock of labor and a larger stock of capital, and the increase in both labor and capital pushes Total Factor Productivity up and wages end up higher than ever.
That's a pretty simple mechanical model, but it makes perfect sense and it says that adding immigrants to the country lays the foundation for long-term prosperity. I think in some ways it will seem more intuitive to people if you think about it in reverse. If a mysterious plague swiftly killed off 5 percent of the population, then in the short term the survivors might benefit. But investment would be depressed and in the long run countries don't depopulate and disinvest their way to prosperity.