Heater door flaps not working?

Okay, that sounds like the mode actuator has failed. On that vehicle it is very easy to replace. First look above the driver's side footwell and you will see a cover that hides all the parts behind the dash and a trim panel on the right side that blocks off the HVAC ducting. Remove those two trim panels by removing the screws and setting the panels aside. Now look up above the gas pedal and toward the front and you will see the mode actuator attached over the mode cam. Remove the three screws that hold it in place. Unplug the electrical connector. Now be sure it is in the defrost position (blowing out the top vents) and install the replacement unit so the pins on the arms are set in the slots on the mode cam. Put the screws in, plug the connector in and test it for proper operation. Replace the trim covers and enjoy the heat.

That was for the blend door, the one that goes from cold to hot. Mine works. The one that doesn't work is the switch that determines if the air goes to the defrost, floor, and or the upper vents.

The mode door is what I indicated that is the one that switches from floor to dash to defrost, the temperature blend actuator is next to it on the side of the HVAC case. Note: the first image that shows both of them and where they are located. Easy to tell the mode unit by the cam that sets under it, the cam is what moves the various doors to direct the airflow. The common failure is the gears inside and the two pins that ride in the cam.

I also have a 2007 Spectra with a good switch as it works. Is it the same? I see the wires going above the blend door switch and behind the black air flow tube, but don't see where they go. Does that big plastic air flow tube thing need to come off?

Yes, the duct comes off and the actuator is behind it. You should see the wiring and the actuator cam behind the duct. The actuator is the same up to a build date of 3-30-2007 so if your 07 was built before that date it is the same actuator. Build date will be on the door tag.