TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.

Once your federal return has been accepted by the IRS, only the IRS has any control.  TurboTax does not receive any updates from the IRS.

To track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

Once you've confirmed your return has been accepted, you can begin to track your refund. The IRS issues most refunds in less than 21 days, although some require additional time. Please see below for more information on tracking your refund: https://ttlc.intuit.com/replies/5340655

After acceptance, but before processing the status may not be available. If you contact the government or try look up your refund status while your return is still pending, don't be surprised if they tell you "no record found." This is normal; until the government starts reviewing and processing your return, they won't have any record of it.

If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.

https://ttlc.intuit.com/replies/4495802