Waiting is frustrating—refunds are taking longer in many cases. These are not normal times. It is not possible for TurboTax to speed up the IRS for you. It seems to be taking longer than usual for them to process returns. They are short staffed; and they are processing millions of tax returns at the same time that they have been burdened with the task of processing millions of stimulus checks. The IRS is not taking calls right now.
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
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. Many refunds are taking longer during the pandemic.
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. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 20 of your Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others
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://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved
Federal and state refunds come from completely separate entities, There is no rule as to which one will come first or how much time there will be between their arrivals.
STATE RETURN
Make sure your state return was accepted: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund