Cards would not work for obvious reasons. A laser mark would be there to stay, but there's no guarantee it woulud be used for ID of aliens--very possible they would use it to know everything about citizens, not illegals.
Have you wondered how the law would be enforced? Can you say "Police State"?
THEN, a national ID card, as tamper-proof as is reasonably available. Once everyone has their card...force all employers to re-verify employment eligibility. Force all new hires to be verified as well.
And the penalty for hiring an illegal: $10,000 per day per illegal PLUS 1 year in jail, per incident.
Then, enforce the hell out of it. High profile stuff especially. Put the CEO of McDonalds in prison and take everything he has...that sort of thing.