From what I understand, you can only pay with a credit (or debit) card having a US billing address.
So, I would contact Turbotax Support through Facebook or Twitter to seek an alternative solution (That is, if you have no access to a credit card with a US billing address). They have an excellent customer service, and are very obliging in these final days before the tax filing deadline.
Good luck.
The link in reply two refers to "foreign credit/debit cards" but the original question is why a debit card linked to a US bank account cannot be used for payment. The owner's current residential address may be foreign but that does not make the debit card foreign. Turbotax: Please change this so debit cards linked to US bank accounts are accepted with a non-US address.
Currently we are unable to accept foreign addresses on U.S. bank or debit/credit cards. The link provided does state "For fee payment, we can only accept Visa, MasterCard, American Express, and Discover cards with a U.S. billing address."