You could require that all workers produce an ID card similar to a credit card for employment. Such a card would be furnished in Mexico; requiring that all Mexicans travel home for the proper documentation. That would cost us nothing. The database derived from such documentation would be forwarded to the United States. Criminals would not get cards.
For the majority of Mexicans, we are not talking long travel times--three hours max. We would set a deadline for all workers to get cards. The bottom line is that no employer could hire a worker without the card.
With the card, the employer tabs in the card number over the phone for worker verification. Any terminated cards would forbid the worker from being hired. With the card you could track where they are working, make them pay income taxes, control voter data bases and set an expiration date which would force all card holders to undergo a naturalization process within a certain deadline--five years, for instance.
Anyone who commits a felony would have their card terminated. The card would have lots of power. With the use of the card, the game would be over for the idea that if you could get enough people to beat the system, you could overload the system. This system would be managed by a simple database system much like what is already used in the membership systems in such retail outlets as Costco. There is no overload of the system. You simply have to get the card to operate in the United States.
Mexico would have to comply with this system. Their economy is dependent on the money these workers send back to Mexico. If Mexico wants that economic inflow, it will cooperate in implementing the system.
O.K., what are the costs for the card system then, and rounding up the 2 million who refuse to leave?