The AC/Heater blower motor on our 2002 Cadillac Deville runs intermittantly. When I had it and the control circuit card out on the floorboard (connected electrically), the blower motor had little torque capability but ran normally and responded to the speed control selection. It took very little pressure to prevent the blower from turning. Is this normal? If so, I wonder if the blower is touching something that prevents it from running. It will sometimes come on if I hit a bump or kick the cover below the glove box.

Check electrical connections for corrosion and tightness. Electric motors normally have pretty good torque.

As a seasoned Cadillac tech, I can tell you with confidence, the blower motor itself is the culprit.
Replacing it is fairly simple, once the actual design is established; there are two types available that year and they aren't interchangeable.
Begin by removing the close-out panel on that side and determine if the blower motor housing is metal or is it plastic. Let me know what you find and I can walk you through the steps to replace it yourself. With a few of the correct tools you can save quite a lot of money.

Sorry for the delay in responding. We have been out of town. I will check the blower motor housing tomorrow.

Jim