I owed Federal taxes and paid on Turbotax, but now I have received a notice from the IRS saying I still owe. The balance was not paid. What do I do?

Your proof that you paid is your own credit card or bank statement, or a cancelled check.  Do you have that?

From what you wrote, it's not clear whether the tax was actually paid. Do you have a record of an actual payment, such as one of the types of proof that xmasbaby0 listed? If no money came out of your bank account or credit card, and the tax was not actually paid, then pay it now. If the tax was paid, follow the instructions in the IRS notice for how to respond.

What exactly do you mean by "paid on TurboTax"? You cannot actually pay the tax on the TurboTax web site. When you filed your tax return, which option did you choose for how you would pay the tax that you owed: direct debit from your bank account, charge your credit card, or mail a check?

Was the IRS suppose to take it out of your bank account?  Maybe the IRS had trouble taking it out.   Better double check the routing number and account number with your bank.  Some banks use a different routing number for deposits and payments.