If you want to split hairs about it, Mexicans have more native blood in them and have 'more right' to the land.
The influx of Mexicans across the borders is much like a tide coming in. It takes time, energy, and financial resources to keep them out. Is it worth that cost? What can Mexico offer the U.S.? (oil perhaps? If the geology is anything like Texas?) The first, most efficient approach is to not fight what is naturally occurring, but find ways to achieve mutual benefits. I was encouraged at the suggestion of an independent Western Hemisphere in political talks a few years back. Whatever happened to that? If the U.S. can find ways to collaborate and integrate resources with Mexico, perhaps we can both become stronger for it? The U.S. could use strong allies in this Hemisphere. There is wisdom in having strong bonds with one's neighbors. If you make an enemy of your neighbor, what happens when foreign enemies become a threat?