Pretty much sure not the sail switch or it would not try to ignite, sail closes with proof of airflow. When you say it ignites , can you hear or see gas flame from outside, and can you feel any exhaust from vent? If it is igniting you may have a blocked exhaust vent, if not may have a bad gas valve. Those furnaces use a Bradford White Valve are usually very reliable but occasionally go bad.
Hope it is an easy fix, could you please let us know how you make out, your fix may help someone else on a cold night. Good luck on a fast repair.