After you file

Was the refund date you are referring to shown on the IRS tracking web site? <a rel="nofollow" target="_blank" href="https://www.irs.gov/refunds">https://www.irs.gov/refunds</a>
If you are referring to a date provided by TurboTax, that is only an estimated date based on average IRS payment guidelines.  Are you having your TurboTax fees paid, from your federal refund? If so, that can delay your refund a few days.