The Social Security trustees projections show that the program can pay all scheduled benefits through the year 2042 with no changes whatsoever. The non-partisan Congressional Budget Office produced independent projections showing that all benefits can be paid through the year 2052. Even after these dates, both sets of projections show that Social Security will always be able to pay a higher average benefit than what current retirees receive, although less than the full scheduled benefit.
In the near term, this diversion of revenue can add between $100 and $200 billion to the annual deficit, depending on the exact design of the program. With deficits already near record highs, it is not clear that the government will be able to borrow this amount without facing much higher interest rates. In at least one country (Argentina), the transition costs from Social Security privatization were enough to push the government into default.
Showing the real numbers on Social Security would take a competent economist only a few minutes, but privatizers want the public to invest trillions of dollars of Social Security money based only on their word. That's not a gamble we should take.