No! Its because illegals are willing to work for pay that is below the mandated minimum wage! If the US did away with the minimum wage, there would be US citizens willing to work for that amount (although in the US, people who refuse to work receive more in benefits from the US government than they could receive from working!)
This is incorrect. It happens because Americans will not do this job for anywhere near the minimum wage, and illegals will do it for far less. The current Federal minimum wage is $7.25. That's $14,500 in a 2000 hour labor-year. I've had farmers already tell me, "Good milkers want $25,000/year. Why should I pay them that?" When I tell them they shouldn't have slave labor on their farms, they just laugh.
The problem is not the employees, the problem is the employer. Farmers are simply NOT willing to pay what farm labor costs and they know that no one will enforce the law.