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.
Make sure your state return was accepted: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
To track your state refund:
Or do you mean the return was accepted for processing but the balance due was not paid ?
If you successfully efiled ….it can be one of 2 reasons :
1) the debit info you sent is incorrect ... expect an IRS letter
If you selected Direct Debit from your bank account to pay the Federal taxes owed, that information was sent with your e-filed federal tax return.
Look at the Federal Information Worksheet in Part V. The bank name, routing number, account number and the date you selected to pay the taxes owed will be entered. If you did not select Direct Debit from your bank account then nothing will be in Part V. Look on your Federal Filing Instruction page for how you selected to pay the Federal taxes owed.
To access your current or prior year online tax returns sign onto the TurboTax website with the userID you used to create the account - https://myturbotax.intuit.com/
When you sign onto your online account and land on the Tax Home web page, scroll down and click on Add a state.
This will take you back to the 2019 online tax return.
Click on Tax Tools on the left side of the online program screen. Then click on Print Center. Then click on Print, save or preview this year's return. Choose the option Include government and TurboTax worksheets
For the State taxes owed the same type of information will be on the State Information Worksheet in Part V of the worksheet and on the State Filing Instructions page.
However most states, if not all, do not allow state taxes owed to be paid by Direct Debit when using tax preparation software. They require the payment by Direct Debit only when using the State tax authorities website.
2) the IRS just has not gotten around to it yet or your bank/CC has not posted it yet.
(If you’re filing your taxes on July 15 and are having direct debit issues, go here.)
During non-peak times, funds are usually withdrawn on the payment date you specify, assuming your e-filed return has already been accepted (received) by the IRS.
If that date happens to fall on a weekend or federal holiday, the funds are typically withdrawn the next business day.
Now, if you filed right before (or on) the busy July 15, 2020 deadline, the IRS may not be able to debit your payment until after the deadline, due to high e-filing volume. In addition, it can take your bank another few days to post the debit to your account.
No worries; as long as you filed your return or extension on or before July 15, 2020 and you selected July 15, 2020 (or earlier) as your payment date, you won't get penalized for late payment.
In the meantime, keep an eye on your bank account — if you still don't see the debit 7–10 days after your return has been accepted, call IRS e-file Payment Services at 1-888-353-4537 or contact your state tax agency, as appropriate.