Be aware of service fees when paying taxes by credit card. If you have a large tax bill, the service fee can be high.
Instead of paying your Federal tax due with a credit card through TurboTax, you could pay your Federal Tax due at the IRS website, if you wish, and the service fee is about 0.5% less there.
https://www.irs.gov/paymentsIf you do that, you'd tell TurboTax you intend to pay by "check" (to fool it so you can continue to file), then you'd go to the IRS site to make the payment. Since you tell TurboTax "check", a payment voucher might print out with your return, but you do not have to mail it if you are paying by some other method.
There are 3-4 different processors to choose from there on the IRS site. Be sure to indicate the correct tax year, the "type" of payment (tax due on the 1040 return), and be sure to print out a confirmation.
It's also possible your state tax agency "might" take credit card payments at their website, too.
NOTE: You can pay your Federal tax due out of your bank account for free using direct debit, either in TurboTax or at the IRS page linked above.