And making an example of three or four would work wonders.
I don't think going for or against CAFTA is going to fix the illegal immigration issue.
If you WANT to modify laws or statutes to "fix" illegal immigration, make it SO expensive for the employers that the possible benefits to hiring an illegal are outweighed by the penalties. Something like fines that no business could weather and stay afloat and/or jailtime at a first offense.
Draconian sure, but it is probably the easiest and cheapest way to do so.
And making an example of three or four would work wonders.