Yes, if you owe the IRS money, the Rebate Recovery credit can be used to help cover what you owe. The state is not affected.
The IRS EIP site states:
The CARES Act limits offsets of Economic Impact Payments to past-due child support. No other federal or state debts that normally offset your tax refunds will reduce the payment. Nevertheless, tax refunds paid under the Internal Revenue Code, including the Economic Impact Payment, are not protected from garnishment by creditors once the proceeds are deposited into an individual’s bank account.
The IRS will begin accepting tax returns February 12 and then begin processing refunds for those eligible.