I paid my federal amount due in full through TurboTax, but just received a notice from the IRS that I had unpaid taxes of $34.38 + penalty and interest. Help?!

what is the reason given in the notice?      I guessing, but most likely, the payment got there after 4/15 or you had an estimated tax underpayment penalty.  

Even if Turbo Tax calculates a penalty on line 23 it is just an estimate.  It's common and expected for the IRS to send a bill for more or even send a refund.  It is determined by when the IRS actually gets your tax due payment which Turbo Tax won't know.