Social Security for Future Generations Act of 2021 This bill increases specified benefits and taxes related to, and otherwise modifies, the Social Security program. Changes to benefits include increasing the primary insurance amount for certain beneficiaries; revising the method for calculating cost-of-living adjustments by using a price index that tracks the spending patterns of older consumers; extending benefits through age 22 to full-time students who are eligible children of deceased, disabled, or retired workers; establishing a new minimum benefit for certain lifetime low-earners; and establishing an alternative benefit based on combined household benefits for widows or widowers in two-income households. Changes to taxes include subjecting earnings in excess of $250,000 to Social Security payroll taxes. No taxes shall be applied to earnings between the contribution base (the maximum amount subject to the Social Security payroll tax, set at $142,800 for 2021) and $250,000. The bill preserves eligibility for Supplemental Security Income payments and other means-tested programs, despite any changes to an individual's Social Security benefits under the bill.