@3dbobby
You canNOT pay your state taxes in any fashion on the IRS's tax payment website.
The IRS is only for Federal taxes.
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Many states do have a way to pay your state taxes due on their own State income tax website.
You'd have to find your own state's Department of Revenue income tax website (I just use a Google search), and then navigate around in it to see if they offer a way to pay taxes due with a credit card. A couple I've seen charge an ~2.5% extra fee for using a CCd.
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When you file your state taxes with TurboTax, you'd just indicate you are paying by check.......then e-file. After that you can pay separately by whatever means you have availble....check in the mail, or whatever is offered on the state's own payment website.