The Right, Just, and Moral approach to this problem:
1. Secure the border. Finish the fence and track down the visa over-stayers.
2. Make it impossible for illegals to work. Mandatory E-Verify coupled with strict penalties for hiring illegals. Companies that discover that illegals have duped them (as happened at the factory I worked for when, in preparing the W-2s last year, the HR person found about a dozen people sharing the same SS#), should have to turn over all the contact information they have for those people to Immigration.