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. https://turbotax.intuit.com/tax-tools/efile-status-lookup/
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
Also, you need to be sure the state return was successfully filed. Here's how:
If you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking at the return status in your Online account at the Tax Home. Does it say accepted, rejected, printed, started, ready to mail, or what?
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
There are over 40 state tax agencies, each doing its own thing. Some states are fairly quick with refunds, while other states (such as WV, WI, NC, GA, LA, AL, and others) can take a long time processing returns--even several weeks--as they crack down on detecting fraudulent returns. The Coronavirus situation may have also added to delays in your state. You may be able to get an idea about how long it takes in your state from the FAQs at your state's tax agency website when you use the tracking FAQ that Critter provided above.