I had a very similar problem with my furnace last year, and it was a defective gas valve. I was not comfortable dealing with that, so I called my furnace guy, he replaced the valve, inspected for cracks / holes in the exchanger (there were none) adjusted the gas / air mix on the burners and cleaned the burners. Furnace works great now. (Well, as well as it has ever worked). -- Gun control is being able to hit your target.