I have the ideal solution to this problem. What do these imigrants want? The "better life" that they can't get from Mexico. They wants jobs, healthcare, and the benefits of an open job market without having to deal with a lengthy immigration process. So here's what we do... we think vertically instead of horizontally, and we build high-speed rail lines from key cities in New Mexico, Texas, California, and Arizona and run them to Canada... the land of socialized healthcare and no immigration laws!
We make the trains available to immigrants and send them off to Le' Canada to enjoy the warm hospitality of their neighbors to the far North. Then we charge the Canadians for the train tickets.