TurboTax never pays your tax. If you first tried to e-file you might have entered bank information to pay by direct debit, which means that the IRS (not TurboTax) takes the payment from your bank account. But when you file by mail you cannot pay by direct debit. You have to either include a check with your mailed tax return, or pay online on the IRS web site using Direct Pay or one of the other options offered. Check your state's web site for how to pay your state tax.
