Higher Wages for American Workers Act of 2021 This bill increases the federal minimum wage, permanently establishes the E-Verify system and requires its use, and contains other related provisions. Specifically, the bill increases the minimum wage to $10 per hour, phased in over three years (five years for businesses with fewer than 20 employees), up from $7.25 per hour. The bill also phases in over three years an increase of the minimum wage for new employees less than 20 years old from $4.25 to $6 per hour, and increases the length of time an employee may be paid this lower minimum wage. Both minimum wages shall be adjusted for inflation every two years. All employers shall use E-Verify to electronically verify the employment eligibility of new employees, with phased-in deadlines that generally require all employers to comply within 18 months of this bill's enactment. This bill provides for various requirements related to E-Verify, including requiring employers to examine and verify certain identifying documents belonging to the employee. The bill increases civil penalties for various violations related to hiring, recruiting, and referring ineligible employees. Repeated violators may be debarred from receiving federal contracts, grants, or cooperative agreements. The bill also increases criminal fines for violators that engage in a pattern or practice of violations. If a state does not provide the Department of Homeland Security access to that state's driver's license and identity card information for E-Verify purposes, that state (and its local government entities) shall be ineligible for certain grants related to public works and economic development.