What should I do if I paid the tax due when I e-filed but I received a notice for the amount due. ?

How did you pay?  Send the IRS a copy of your bank statement or credit card showing the payment.

Your only proof of payment is your bank statement or credit card showing the payment coming out.  Turbo Tax only passes your bank account number to the IRS or state for them to take it out of your account.  (Most states do not let you pay by Direct Debit so you have to mail in a check or go directly to the state's website to pay).  And some banks use different routing numbers for deposits and payments.  Double check the number you entered with your bank.

Is the IRS billing you for the full amount or just some more interest or penalty?  

How did you pay the taxes owed?  Check, credit card or direct debit from your bank account.

If the taxes were paid, then you should have a canceled check, bank or credit card statement showing the payee and the amount paid.  These are your proof of payment.