The problem is a current state of an always-fluctuating market, and if you ask me, I'd bet overregulation of businesses is probably more to blame for the resulting illegal workers. Illegal Mexicans are a symptom.
Take the gruesome job of meatpacking. The majority of Americans are probably much too finicky to hack animal carcases for a living, as they see it, even if it earns them a decent living.
Illiegal immigration ala cheaper workers is not a pressing make-or-break issue compared to terrorism and the U.S.'s place in a dynamic and violent world. Sure, terrorists find it easier to sneak in under lax immigration laws, but it's an entirely different kind of immigration issue than illegal Mexicans, and a hell of a lot more important!
Really? I used to know Americans who gladly did that kind of work.
".....all the fences and laws in the world will ultimately fail..."
Strange remark. The areas where fences are erected have noticed a measurable decline in illegal crossings.