How do I sue turbo tax for messing up my owe amount projection?

i doubt whether you can for a projection. however, if the return filed understated your liability and it was due to a Turbotax calculation error 

Intuit works to ensure the accuracy of the calculations on every form prepared using TurboTax. If you are a registered user who has updated your copy of TurboTax with the most recent update available prior to filing your return and reviewed your return for reasonableness and you pay an IRS or state penalty and/or interest solely because of a calculation error on a form prepared using TurboTax, and not as a result of, among other things, your failure to enter all required information accurately, willful or fraudulent omission or inclusion of information on your tax return, misclassification of information on the tax return, or failure to file an amended return to avoid or reduce an applicable penalty/interest after Intuit announced updates or corrections to TurboTax in time for you to file an amended return, then Intuit will pay you in the amount of the IRS or state penalty and/or interest paid by you to the IRS or state. (A "registered user" is a user who either registers his/her TurboTax license purchase with Intuit, or has purchased a license to use TurboTax directly from Intuit). The Accurate Calculation Guarantee does not apply to tax forms completed in which the data is entered directly by you onto the form, rather than through the use of the in-product TurboTax interview guidance. You are responsible for paying any additional tax liability you may owe and providing any other information Intuit reasonably requests to validate your claim.

If you believe such a calculation error occurred, you must notify Intuit as soon as you learn of the mistake (and in no event later than 30 days after the penalty or interest is assessed and within the applicable federal and/or state tax filing statute of limitation) at https://ttlc.intuit.com/community/charges-and-fees/help/how-do-i-submit-a-claim-under-the-turbotax-1... or by mail at Intuit Inc. TurboTax Accuracy Guarantee Analyst, 2800 E Commerce Center Place, Tucson AZ 85706. Intuit will then contact you to resolve the issue. To validate the claim, Intuit may require your TurboTax tax data file (mandatory if you did not electronically file), a copy of the IRS/state notice, and any other documents to support the income, deduction or credit.

@lauderback13 - before sueing, what do you have on Lines 28 and 30 of Form 1040?  Those are the Advance Cbild Tax Credit and Recovery Rebate lines.  What I have found is EVERY post where the tax return has been adjusted is because of the taxpayer's failure to correctly enter what they already received from the IRS,

if you enter the wrong information, TT is not liable for that.

I can walk you through this if you post what is on these two line items.