To be fair, many against illegal immigration push for going after companies who hire illegal immigrants. A lot of those many would prefer to go after the employers first, because you solve a problem at the source and not by treating symptoms. E-Verify and employment law are supposed to do that, if there is no economic incentive then most illegal immigration stops.

As for seasonal migrant workers, there are laws enabling them to do it legally. They need desperately need to be updated and expanded, but the legal groundwork is there.