[DB]

Get rid of their employers and don't allow them on welfare and they will have to leave.

[B Knotts]

Yes, I agree that employer sanctions must be part of the equation, as well as a foolproof (or nearly so) means of pre-employment status screening. Right now, it's almost impossible for an employer to check on someone's status before they're hired if they provide forged documents.

[Tokra]

Get rid of their employers and don't allow them on welfare and they will have to leave

Once again - they can't and don't get welfare. Only legally admitted aliens who have been in the US for at least 5 years are eligible for welfare.