Most of what I have read on the impact that illegal immigration has on wages conforms to what Matthew Yglesias is saying. His final point makes perfect sense.
I do, however, agree with Sir Charles that both undocumented immigrants and those who compete with them in the labor market are seriously disadvantaged by the fact that, due to their immigration status, they have no meaningful way of enforcing their legal rights. This is one of several reasons to favor comprehensive immigration reform.
If those who claim they are against illegal immigration because of depressed wages then they should be the ones most in favor of comprehensive reform that creates a pathway to citizenship for those working here without authorization. By mainstreaming this underground source of labor, you undercut their greatest comparative advantage in the workplace. Yet, I suspect that those who use he argument of depressed wages really have an different motive.