If you have done this in the past, then it may still be an option. It may not be an option directly through TurboTax though.
As you are completing your return and choosing your filing options, you will see what payment options exist for a state balance due. If you do not see 'pay by credit card' as a choice, you could select pay by check and then check your state's department of revenue web site for a place to make your payment directly to them using a credit card.
Use the information in the following TurboTax article to contact your state Department of Revenue:
When I select the continue button it prompts me to pay for turbo tax, but I bought it at a store
I do not get the option to enter the confirmation code
It depends. If you owe federal and state income taxes, you may use auto debit from your checking account entered while finalizing your income tax return. If not, you can make a payment through the IRS website (federal) with your credit card. You may access your local state revenue to make state payment