Social security, unlike all the rest of the US Government welfare programs, draws from a separate trust. It currently has roughly $3 trillion in the trust. When you pay income tax, there’s a portion (usually noted on the paystub) that goes directly to the trust. If they continue current payments, the income of everyone stays the same, and the tax percentage stays the same, then it will run out of funds after a while (currently predicted to be 2035).

However, I would bet pretty strongly that one of those constraints won’t hold - probably the amount paid out to each person will be lowered, although the tax percentage could also increase.