I don't get the alleged "tax paying" part of this. If they are here illegally, exactly how are they legally paying taxes? If they supply an SSN to the employer, then we have felony document fraud and identity theft. If they supply an IRS administered TIN, then are they working as 1099 contractors (and filing and paying quarterlies along with both sides of FICA and Mediscare)?
When they pack dozens into a house designed for a family of four, they are stressing the sewers and violating deed restrictions. With high density crowding in homes, their cost per person in the form of property tax (either direct or through rents) is relatively small. Then they wire the money out of the country that is money not spent on sales taxes, investment income taxes et al.
Probably the only taxes they are paying is in alcohol and perhaps gasoline taxes. And I doubt that much money is being raised by these taxes to cover each of their children being "educated" at the average cost of $12k per year in the government day care centers.
The Social Security administration has a big account of SS taxes paid that do not match anyone. The new technology suggested will ping a proffured SS# against a data base much like credit card approval works. This will flag numbers that are fraudulent or reported missing. It will infringe on your privacy just about as much as presenting your Master Card does. It will help catch criminals for deportation for those who like that idea.