Good luck if you are trying to get a backcountry permit:
Backcountry Camping Reservations:
The online backcountry reservation system is unavailable due to the shutdown, so backcountry reservations are currently being accepted by phone at (865) 436-1297. Because of the uncertainly as to whether or not the park will remain open past October 20th, reservations are only being accepted for trips beginning on or before Saturday, October 19. A high volume of calls is anticipated. If you reach voice mail when calling, please leave your name and phone number so that your call can be returned as soon as possible.