The immigration debate suffers from overgeneralisation. Illegal immigration is a different problem from legal immigration. And short-term skilled migrants are unlike long-term skilled immigrants. Short-term migrants, i.e. those with no intention of staying in the U.S. long-term, probably depress American wages. Skilled immigrants aiming for residency, and certain classes of unskilled illegal immigrants, appear to add net value.
(Exhibit A of our system's self-destructiveness are international students at American universities being refused residency on graduation.)