Where are you entering the number of days you lived in NC? (And....2024 was a leap year with 366 days...)
Please clarify, per @xmasbaby0's question above- where are you entering this information? Typically, you will not be asked the dates you lived in the state if you were a full year resident- the dates are usually to figure your time in a state for part-year residents. Make sure your "About Me" information has your correct state, as well as the NC input should show you were a full-year resident.
I had the same issue but it might be caused by a different situation than yours. I had to enter two lines under Schedule A 1b(2) because I was taxed at two different tax rates (8.25 and 6.25) during the year. I had entered 01/01/2024-12/31/2024 on both lines and that caused my problem which generated the 366 days error. I changed the dates to split the year based on when I made the purchases. For the 8.25 tax rate, I used 1/1/2024-11/30/2024 and for the 6.25 tax rate I used 12/1/2024-12/31/2024 because I made that purchase in December. That fixed my problem and allowed me to transmit my return.
This might be a workaround. Use two lines for 1b(2) and put the dates for half the year on one line and the other half of the year for the second line???? It would be helpful if Turbo tax modified their software to allow for leap years. Hope this helps.