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.
I started a new thread in the "In the Backcountry" area, but worth adding to this thread as well..
https://smokiespermits.nps.gov/index.cfm is up and running. It went online sometime between 6 AM and 9 AM EST
I made a reservation and got my order number. When I entered my order number on the page https://smokiespermits.nps.gov/gsmbctransactions.cfm
I received and error, "Your transaction information could not be found"
I called the backcountry office (865)436-1297 and Ranger James W emailed me the PDF Reservation form.