The state income taxes withheld on your W-2 (Box 17) is an estimate that you and your employer made at the beginning of the year (when you filed your W-9 with your employer) of how much state income tax you would owe.
Now we are at the end of the year and you have entered all your information into TurboTax, so the software has calculated what you actually owe.
Your estimate on the W-2 is almost certainly high or low. If your estimate was high, then you will likely get a refund. If you estimate is low, you will likely owe tax.
The number in Box 17 is not the amount of tax that the state assesses, but only how much was withheld to pay for your assessed tax.
Also note that as your income increases (adding a second W-2), your effective tax rate also increases, so what was enough withholding for one W-2 isn't enough for the second one.