Since I am not from OH I don't know how the Ohio voters feel about him as governor. He claims to have balanced the budget. They would know if he did or not
I would say that he has done a good job of balancing the budget. That is not to say the budget is totally balanced. Really, how many states have a truly balanced budget. But it was really bad before Kasich. Now its reasonable. Franking helped for a while. But now its less helpful. You can think of Kasich as you would a Jack Kemp or Phil Graham.