Had that happen to me a few years ago while fishing for Channel Cats. Had a pole tip just barley moving and after watching it for a couple of minutes I decided to set the hook. When I set the hook it felt like a small Catfish.
After the second or third crank of the reel, the rod bent down almost to the water and drag started to peal. After a 10 minute fight a big Yellow Cat finally let go about a one or two pound Channel.
The Yellow swam off.
As for the Channel Cat it was another story!