My basic tax return was so far off

this public forum has no access to your data or return, so we do not know what was changed. Might even be a scam. if you have doubts contact the DOR using their website and not any phone number in the notice.

you can also submit the notice to

The Audit Defense service is provided by TaxResources, Inc., also called TaxAudit.com, in partnership with TurboTax. If you paid for Audit Defense and you received a notice, call TaxResources, Inc. at 877-829-9695, or report your notice on their website at http://intuit.taxaudit.com/. Do not contact the tax agency until you have spoken to TaxResources. They may contact them on your behalf.

if you did not purchase Audit Defense at te time there could be a fee.

if it is determined to be a TurboTax calculation error, you can submit to TurboTax a claim for penalties and interest. You are responsible for the additional taxes. 

Here are some possibilities, although by no means exhaustive:

• W-2 Withholding Mismatches. When importing or typing in two W-2s, a typo in Box 17 (State income tax withheld) or accidentally assigning both W-2s to the same spouse can cause New York to think you claimed more tax payments than your employers actually sent them.
• Out-of-State or Multi-State W-2s. If one of the W-2s was earned in another state (like New Jersey or Connecticut) or shows wages in Box 16 for multiple states, New York may have disallowed a resident credit or adjusted your allocated income.
• Itemized Deduction Adjustments (Form IT-196). Your Rocket Mortgage Form 1098 only reduces your New York taxes if your total itemized deductions exceed the NYS standard deduction ($16,050 for Married Filing Jointly in recent tax years). Furthermore, New York disallows or limits certain deductions—such as mortgage insurance premiums (PMI) or property taxes exceeding federal caps—on Form IT-196.
• NYC or Yonkers Local Taxes. If you live in New York City or Yonkers—or moved into or out of those cities during the year—and the local tax checkbox or resident months were missed on Form IT-201, the state will automatically bill you for the unpaid local tax.
• Missing or Unmatched Estimated Payments. If you accidentally indicated that you made an estimated tax payment or applied a prior-year refund that New York has no record of receiving, the state will remove that credit and bill you the difference.