I live in a SoCal city with alot of illegal immigrants. And when I say alot, I mean thounsands, if not tens of thousands. There is no way to deport them all or coerce enough of them to self-deport in numbers that would make any real difference.
That being said, there is material to work with. Many immigrants are fiercely entrepenurial and will go where the money is. They are also culturally conservative and have many family members in the military.
Finally, they keep wages low that should be low (e.g. gardening, housekeeping, fast food).
You are dead wrong on that issue, look what is happening in Oklahoma.