Once you prepare your return using TurboTax, you have a rough idea , if you owe anything. IRS recognizes the 15th of April as the settlement date for amounts owed. The extension is only for filing not for paying. If you owe when you finally file, you will be charged interest from the 15th of April.
You can make an estimated payment ( check or direct debit ) along with the filing of the request for extension.