You cannot make a payment through TurboTax nor can TurboTax contact the IRS on your behalf.
If you agree with the IRS notice then you can pay the federal taxes owed on the IRS payment website using Direct Pay - https://www.irs.gov/payments
If you disagree with the IRS then follow the procedure in the IRS notice you recieved.
IRS website for a CP14 notice - https://www.irs.gov/individuals/understanding-your-cp14-notice
