Suburban Furnace NT-20SE not working

Thanks so much for the info!! I figured it out! It was the very small gauge wire that they ran under the camper up to the thermostat. The first spot that I checked had a spot worn through the wiring. I taped it with electrical tape and it fixed it, but the thermostat is still fried. I am going to get a digital one from Wal Mart or Lowe's.

A bad fan motor would have nothing to do with an overloaded thermostat- depending on the age of the unit, it could have either a fan relay or fan control circuit board that the thermostat controls. Smoke pouring out of the thermostat can indicate the anticipator is set incorrectly- if it is set way too high, it will smoke. If the thermostat wires are fine, I would try simply connecting them together.
Not sure about the light dimming, but given the thermostat wires are so small, there cannot have been to large a draw through them. It could be 2 problems- thermostat and blower.

I did try that and it had some resistance at first. It did not spin as freely as I thought it would, but that was using a long rod to reach back there with the front cover off. I mess with the delay setting on the thermostat and it sparked heavenly when I touched it. Is there a way to test the time delay relay? Where is it located in the furnace box? Thanks for the information!!!

You could try spinning the fan blade with your fingers with power off to se if it spins freely.
Thermostat has very little power to cause them to fry. Could be issues with time delay relay that would apply more power to it.