No TurboTax does not pay your extra tax owed. If there was an error in TT's calculations that resulted in your problem, TT pays the penalties. TT never pays your tax owed
ACCURACY GUARANTEE
TurboTax provides do-it-yourself tax software. TurboTax guarantees the calculations done by its software. The information entered into that software is data entered by you, the user. TurboTax cannot and does not check that information against any outside sources, so TT cannot know if you entered your information completely or correctly. It is up to you to enter all of your information correctly and completely, and to check your tax return before you file it. If you forget to enter some income, or enter it incorrectly, enter it in the wrong place, etc. then you may end up owing additional tax to the IRS and/or state. TurboTax does not pay the additional tax you owe. If TurboTax’s calculations were incorrect, and you owe penalties and/or interest, then TT will pay the penalties and interest. The tax due is always owed by you, and must be paid by you.
If you need to enter a claim for the accuracy guarantee:
I RECEIVED A LETTER FROM THE IRS/STATE
TurboTax does not receive any information from the IRS or your state after your return was filed, so no one at TurboTax knows about a letter you received from the IRS or the state.
(what the letters from the IRS mean)
I GOT A LETTER FROM THE IRS
https://ttlc.intuit.com/questions/3605673-i-got-a-letter-or-notice-from-the-irs
I AM BEING AUDITED
If you purchased Audit Defense:
https://ttlc.intuit.com/questions/2924451-i-bought-max-or-audit-defense-and-now-i-m-being-audited
AUDIT SUPPORT
TurboTax has a special phone number for help with IRS/state tax letters, which will be easier than going through regular Customer Support. At the page below, click on the blue button that says "Get Help from TurboTax Support". Then it will ask you what tax year is your letter. Then it will ask you what the letter concerns. Then it will show you the phone number during posted business hours.
https://support.turbotax.intuit.com/irs-notice/audit-support/