First give employers the tools to determine if workers are illegals, then fine employers for each illegal worker and require them to pay for all the social services used by their illegal employees and their families. Jail time for repeat offenders.
A few company owners and presidents bankrupt and serving time in jail will focus the minds of other employers on this issue.
I remember when I worked in HR for a construction company. You can't tell the difference between a fake ID and a real one. SS cards and fake id's can be bought on any street in any city. It's a real problem. In an ideal world, it would be easy to fix. But I do believe this problem is multi-faceted. We need to:
1. Put up a wall
2. Enforce our current laws which include fining businesses as well as deportation
3. Deal with the current "illegals" who have had children in the US.