The federal tax refund date on the TurboTax Tax Home web page is only an estimate based on the IRS target of issuing a federal tax refund within 21 days after accepting the federal tax return, it is NOT a guarantee.

Once a tax return has been Accepted by the IRS or a State, TurboTax receives no further information concerning the tax return or the status of any tax refund.  

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions