Here's the thing: illegals are bad for business. Oh, don't get me wrong, I'm for fighting illegal immigration by making legal immigration easy and painless and, most importantly, transparent. Right now it is a years-long nightmare of bureaucracy that's soul-wracking to endure if you have plenty of privilege, let alone for a farm worker. Immigration is fine.
No, the reason illegals (as opposed to people from Mexico who came to the US nice and legaly) are bad is because they can be mistreated more easily. One form of mistreatment is social isolation (meaning they can't unionize properly) and another are extremely low wages. They can afford to work for bad wages because going back home, where what they earn is (barely) worth enough, is worthwhile if there's sufficient despair. A higher income version of that also exists with, say, tech jobs.
American business, therefore, gets addicted to this cheap labor and sets up a business model which only ever works if the labor is incredibly cheap which means altering it is ruinous. This results in low employment and stagnating wages for those that do find employ (aside in a few privileged professions) leading to low aggregate demand leading to, ah, what's the term of art? Jobless recoveries. That's the one. This low aggregate demand is propped up using cheap credit and artificially depressed price of oil (Over $5 in Europe which is probably still not enough to offset the hidden ecological cost), to the general ruin of us all eventually.
Quitting it cold turkey will tank the economy. Quitting it piecemeal will ruin whoever starts it first (thus making for abundant incentive not to be first). Qutting it under a planned program is impossible because anyone suggesting it will be branded a Stalinist/Racist/Both depending on their political flavoring.
Solution? Hell if I know.
 And, seeing as I'm from a poor country too, I can afford for that matter.
 Of course, most of this cheap labor is actually abroad via NAFTA and such.