Most Federal REFUNDS are issued within 21 business days of the return being accepted by the IRS.
Please keep in mind that once you e-file or mail your return only the IRS has any control over it.
The IRS will notify TurboTax when your return is accepted, but there are no more updates given for the next 2 stages of Processing and Approval.
You have to go to Where's my Refund to get any further information.