It looks more like a Carolina Wolf Spider, the largest spider indigenous to N.C., to me. If I search for nursery web spider, the images are nothing like this spider.
Mark Sturtevant wrote:
The spider is a female nursery web spider (Dolomedes tenebrosus). Very big and it can run pretty quickly in short bursts. But they will really just run away from you. They are good mothers. This large female will make an egg sac and carry it under her body while holding it with her fangs. When her babies are hatching, she will place it up high somewhere in a 'nursery' of spider webs. There she will guard it. She might be doing that now, so her nursery might be in the tree hole.