I used to work at a school for the kids of migrant laborers. The dads don't really trust anything that looks like "the system." Going into an office - that is how you're going to get into trouble with the INS.
However, keep in mind that day-workers and agricultural laborers aren't necessarily illegal. Where I was working, most of the people working in agricultural labor were migrant workers, but were also actually legal U.S. citizens from border towns in Texas.