TT flags this as a problem. every state that I've ever worked with that had an income tax required an ID # so it could match the withholding you claimed with what the employer showed. it could be that the copy it filed with the state had an ID # in which case getting it from the employer would be adequate without it supplying a corrected w-2. if the state's copy doesn't have an ID #. likely the state will contact the employer but no telling when that would be - inform your employer to get things moving.
My employer has always left this field blank on my W2 but this year it caused my electronic submission to not go through. When I contacted Turbo Tax help desk, they found I could enter anything as long as it follows my normal state layout. (I entered 1234 56780 and it accepted it).