The induction motor on my forced air furnace just keeps running.

Is that right?

The inducer fan keeps running until heat is satisfied and cycle is complete. If inducer continues to run after heat cycle, the inducer fan relay on the control board may be stuck or bad. If you are lucky you may be able to unsolder and then replace the relay but usually it is the board that needs to be replaced. Find the relay and tap it. If the inducer goes off, you have found the problem. In many cases, the relay contacts get pitted and stick together.