HARTFORD, Conn. — Dorry Clay, a small business owner unable to save for retirement, is counting on the Connecticut legislature to establish a state-run retirement savings account accessible to millions of workers.

Lawmakers in Connecticut and other states are responding to a widespread loss of private-sector pensions, a lack of access to employer-sponsored retirement accounts in smaller businesses and stagnant incomes that make it hard for workers to contribute to their own retirement plan or company account.