Improve e-verify, but the real key to stopping illegal immigration and forcing those already here to go home is through workplace enforcement -- primarily raids, fines, and jail for the employers and the illegals.
And it doesn't require this enforcement on a massive scale. Compliance can be gained in the same way that the IRS gains compliance from most taxpayers -- the threat of these punishments. In the same way that the IRS only audits a small percentage of taxpayers, ICE and other enforcement agencies can simply choose a small targeted and heavily publicized team of prosecutors and investigators to bring a a real threat of serious consequences which would force a much higher level of compliance for most employers.
Remember when Bush finally started putting some heft behind the prosecution of illegals in the workplace after his amnesty bill died? Illegals actually started going home and would have continued if the policies hadn't been ended by Obama. When people fear the possiblity of losing everything, however remote that chance might actually be, they are much more likely to comply with the law.