From a report issued by Social Security's Office of Chief Actuary, issued in response to a request from Senator Marco Rubio:
Beyond the taxes paid and benefits received by unauthorized workers, the larger effect on the long-term actuarial status of the OASDI [Old Age, Survivors and Disability Insurance] Trust Funds derives from the children born in the U.S. to these immigrants. These children are natural born citizens and add to the growth in the overall U.S. population. This contribution to future generations of workers is the largest part of the effect on the actuarial status both for legal and other immigrants. ...
While unauthorized immigrants worked and contributed as much as $13 billion in payroll taxes to the OASDI program in 2010, only about $1 billion in benefit payments during 2010 are attributable to unauthorized work. Thus, we estimate that earnings by unauthorized immigrants result in a net positive effect on Social Security financial status generally, and that this effect contributed roughly $12 billion to the cash flow of the program for 2010. We estimate that future years will experience a continuation of this positive impact on the trust funds....
Individuals who enter the country as unauthorized immigrants and remain in that status for life are relatively unlikely to receive benefits from the OASDI program. Those who work in the underground economy have no basis for expecting to be entitled for benefits. Those who have worked and paid payroll taxes without a matched SSN [Social Security Number] will have had their earnings placed in the suspense file and will have only a relatively remote possibility of obtaining credit for these earnings for the purpose of becoming entitled to a benefit. The relatively small and declining number of unauthorized immigrants who have an SSN with earnings credited in their name, may receive benefits in the uture. However, to receive benefits they must meet the following three conditions: (1) work long enough to acquire insured status under the program; (2) receive legal work authorization at some time; and (3) receive legal resident status for the time of their benefit entitlement or, if not, are willing to leave the U.S. to receive a benefit.