Hope this isn't like my 04 Cavalier MVAC mode door problems, door was jammed, wife tried to force it and bent the cable, a rack and pinion thingy to operate this door.
It wasn't too bad, screws held in the upper dash panel, removed that and the duct work to see where a piece of foam was attached to the mode door with double sided sticky tape. Not sure what GM was thinking on this, with 195*F air blowing that dries up that sticky tape. Nothing wrong with that foam, it just fell off. First I tried weather strip cement, that didn't hold either. Second time, since only the perimeter of that foam was making contact, cut out and aluminum plate and held down that foam with real screw metal screws.
Replacing the cable wasn't as easy, actually could have dipped it in a solder pot with a special flus to stiffen the end, okay for pulling, not very good a pushing. But for 12 bucks replaced it with a new one, had to remove the front seat and console, and radio to get at it.
See on the Cruze, its all electric with push button controls, and now they have airbags in the front seats, so those are no longer easy to remove. Just hope they figured out a better way to mount that foam. Looked through the shop manual on this thing, line drawings are so poor can't tell how its mounted. But hope they used screws instead of double sided sticky tape.
Let me know what you find. Pushing a button is a lot easier than turning a knob, but hope the price of that is not a nightmare if you have problems with it.