How do i know federal accepted the payment i sent via your tax filing?

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TurboTax can only e-file / transmit your return. The  amount due is  debited by the taxing agency from your bank account ( if that is what you selected ) or by check you have to send in.  Which path did you select?  

If you did not select direct debit ( including providing your bank details and a date for debit ), then you need to either send in a check for the amount along with a 1040-V OR go to www.ir.gov, look for Payments, EFTPS and do the needful there ( it allows you to pay by Credit Card, Debit Card or direct debit from your bank.