A Mexican man can work HERE for three months and live on that for the other NINE months in Mexico.
I know this because I lived and worked in Mexico City for two years. Most of my relatives are there. I have over 50 cousins there.
They DON'T want to be gringos but they know that they HAVE to speak English, so they have TONS of schools and classes teaching English.
As for work, there are HUGE numbers of Mexicans who live on the Mexico side and work north across the line, doing whatever. The women are often house cleaners. The men will do whatever.
There are thousands of braceros who are brought into California every late summer to harvest crops for the American growers. AMERICAN workers won't do it for less than minimum wage, and sometimes, NO amount of money can get Americans to pick fruit. Why should they when they get the free handout, without lifting a finger, from Uncle Sam via welfare?
Finally, the DRUG BUSINESS is so huge because the American market is so huge. We give them the impetus to grow and transport all the illegal drugs.
In my area many of the illegals are Peruvian and Ecuadoran, with some Central Americans as well. I know across the country the majority are Mexican, but eventually Mexico will run out of people to export; today 1/10 of all people born in Mexico already live in the US.
The bracero program is monitored/administered by our government (at least it used to be); I remember when schools were set up for their children during their seasons here. Americans will do any work when the wages are determined by true supply & demand; the agricultural sector simply skirts that to keep labor costs low. Long before Mexicans were swarming across the border, Americans worked as farmers all over this country.