False choice. Just have national ID cards with a swipe function, and send employers who hire illegals to jail when caught through random audits. When one wants to kill a tree, one doesn't do it by plucking off the leaves, one by one.
We already have laws on the books punishing employers who hire illegals. The laws are not enforced. The number of employers investigated and/or fined is miniscule.
It's illegal for an employer to question an employee's purported legal status. That's discrimination of some odious sort.
Why put the responsibility of law enforcement on private business?
Employers are already suffering from too many government regulations.
By the way, conservatives don't hate employers, that's labor unions and Buchanan.