"Is a national registry of US Citizen finger prints with random mandatory finger print checks at places of employment the only surefire way to deport illegal aliens?"
Consider; we have social security cards , that should be enough to suffice along with federal law in place that demands one be used if an employer and employee do business.
The employers and the IRS can cross check numbers, if one is in use already, and joe south amercia is applying for job hauling trash using the same ID as a public school teacher in Montana, it doesnt take the technology and the empire of Bill Gates to determine something is wrong in river city.
The federal government knows now when social security cards are being double dipped, they even maintain lists, but refuse to do anything, since why should they if they can collect on both? Cleary there is a conflict of interest.
The other scenario is those employees and employers who do not use any social security cards, and are participating in black market labor, analogues to prostitution. Out cities are turning into red light districts, where illegal services and money is being transferred. However, if a citizen tried to hire other another citizen and didnt pay social security, federal and state insurance fees, the employer and or employee would be hauled off to jail.
In summary social security cards and the IRS do a good job of monitoring legal business for US citizens, It doesnt take a lot technology to realize that illegal services are being performed, but like prostitution thought all of history the illegal service black market industry never going to be stopped. Yet it can be controlled at least and it can be frowned upon , up to the community to enforce laws of decency, (moralistic values and anti-slavery), but as it is our hands are tied by the conflict of interest that our politicians have in dealing with the situation, by simply not enforcing a valid social security card be required for employment.
No Jobs, then they go home, easy as no ticket, no laundry....