"The employer could verify social security numbers every time they got an Hispanic applicant, but then they'd be sued for discrimination under Title VII."
You sure about that? Ever heard of the Basic Pilot program?
Actually, Basic Pilot went into effect since I last looked at the problem. Before that, you could use other means to verify social security, but it cost something, and if you didn't do it for everybody -- just those who "looked" illegal -- you could be sued.
It looks like Basic Pilot is a good idea. Easy and free. It should be mandatory.