"Nonsense. That's like saying that the only way police can be expected to tell the difference between law-abiding citizens and crooks is for the former to carry an official I Am Not A Crook card (with an engraved holographic seal depicting Richard Nixon, perhaps)."
If you can tell me how an employer can be expected to distinguish between an American citizen with a foreign accent and poor command of English, and some illegal alien who has perfect command of English and dresses and acts like an American, I'll agree with you.
The illegal alien problem, by and large, isn't driven by employers who were honestly fooled after a routine check of SSN, green-card records, and the like came back OK. It is driven by employers who simply don't bother, or who actively prefer to employ illegals (because they can be threatened with deportation if they complain about unsafe conditions, lousy pay, etc).
Exploiting the issue to sneak in the government's pre-existing your-papers-please agenda is unacceptable.