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!
Before you can put this into effect, you have to have a nonforgeable form of ID. As it is, there are a multitude of acceptable IDs, and the employers can plausibly say that they're not experts in detecting frauds. As long as the person can present something that's on the approved list, and it looks good enough to a layperson, the employer is off the hook. Other than Tyson, I haven't heard of a prosecution of an employer.
"I'm not an expert at checking IDs for forgery, how come the GOOBERMINT didn't pick up on it when they gave this guy a DRIVER'S LICENSE?"
Problem solved!
Not.