Cannot fully turn off heater in 1994 Dodge Caravan

When I move the temperature lever in my air conditioned 1994 Dodge Caravan all the way to the left (recirc), I get cold air - because this also closes the heater valve. If I move the lever just to the right, to cold-but-fresh-air, the lever pops about 1/2 inch further right. I took the controller out and saw that it’s not pushing the temperature cable all the way in (to full cold). I can push it in by hand, but the next time I cycle the lever the same thing happens. Before I spend time and money, do I need a new controller, a new cable, or something else? Is there some sort of adjustment on the cable that could help?

Drip some oil onto the cables and work them back and fourth a few times. If that doesn’t help it might be the valve itself that’s sticky.