Regime change in Mexico would accomplish it, too. Throw out the greedy corrupt politicians and police, and make it possible for the ingenuity and drive that gets Mexicans here to bear fruit for their labors in their own country. We wouldn't need a border patrol if Mexicans didn't want to leave Mexico.
Sometimes containment is the answer, as in the Cold War. Other times, it requires a more robust approach, as with Iraq (and Japan, in the not too distant past). I can't really see us trying to do anything about this until after we've got the Middle East stabilized, though.
Regime change...I wonder if the U.N. would approve : )