The first order of business in getting the illegals out is verifying who is and who isn't an illegal alien. Notice that a lot of folks say "THEY have to prove they're here legally, I don't." On what basis do they say that?
IMO the draconian part comes in sentencing of offenders. Anyone caught employing illegals would pay a hefty fine the first time, the second time said employer goes to jail. Anyone caught fabricating ID's gets the chair.
Problem solved!