Living in San Diego, surely you're aware of the tens of thousands of Mexican workers who cross the border daily to work as housekeepers, gardeners, etc., many of them paid cash under the table. In my business there I frequently provided services to the uber wealthy, and many of them had foreign born, non-English speaking staff, nannies, maids and the like, living on their properties. One could reasonably assume most were not citizens, had no papers, no income deductions, and in many cases I knew that for a fact. I also had occasion to hire subcontractors, and it was not uncommon for them to offer me a discount if I paid them or their employees in cash, wink nod.
It's a dirty little secret that many of the folks who give lip service to cracking down on illegal immigration, benefit from employing workers illegally at lower wages - while avoiding deductions, employee contributions and those pesky laws governing employment practices. Like so many things, when it comes right down to it, it's plain old greed and the desire to maximize profits. The supply of illegal workers meets the demand for cheap labor, and these practices drive down wages and benefits for the legal working class.
"But Americans don't want to do those jobs", is a common argument. Well yes, they would, if you paid them a decent living wage with benefits. No, most Americans don't want to pick tomatoes for $10-12 an hour; it's hard, hot, back-breaking work. But I bet plenty would if you paid $20-24 an hour with benefits. If you're a worker with virtually no living expenses in a trailer with 10 other guys, who's sending all the money back to his family in Mexico - where it's worth many times what it is here - it's a no brainer. "But that would drive up the cost of groceries", you say. Pffftt! I say. Americans are too fat already, we have the cheapest food in the world, and we throw half of it away. Plus I'd rather pay a few cents more for a tomato than live in a country where workers are exploited, whether they're legal or illegal.
Despite all the posturing, the truth is that Mexican nationals, the Mexican government, individual Americans, and especially American business all benefit from the status quo. After oil exports, remittances sent from workers in the U.S. are the second largest source of foreign revenue for the Mexican economy!