Both illegal immigration and skilled immigration problems will be gone eventually with no action if the opportunities are no longer better here. Do the majority of Americans really want that?
If I'm Mexican, the US is a lot cheaper and easier to get to than China or India. You're right about the skilled immigrant problem though. That will hit the US hard.
The Mexican economy is doing very well. What happens if economic growth in mexico creates greater demand for unskilled labor, reducing the incentive to work in the USA illegally.
There is some research that shows that this could happen in the next decade.