The academic literature* shows much, much larger productivity and income gains to those who migrate to richer countries than any negative effect to native workers. Even if an influx of immigrants depressed some existing Americans' wages by a small amount, that delta would only pale in comparison to how much better of the immigrants would be.
Do you oppose efforts to educate more American's as computer scientists? This too would "depress" the wages of existing computer scientists but you would (hopefully) find it abhorrent if someone used your "wage depression" logic to stop teaching CS in inner-city schools.
Unless you think that the lives of non-American's are not worth considering, these hugely positive impacts of immigration should be part of your calculation.
* http://www.ssc.wisc.edu/~jkennan/research/OpenBorders.pdf?ne... http://www.cgdev.org/files/1425376_file_Clemens_Economics_an...