Just to follow up, I contacted Nissan consumer affairs at (877) 664-2738 and opened a case. They were able get the parts shipped quicker than what the dealer was told.
The timeline for me was
11/20 - start leasing 2013 SV
12/3 - PTR heater did not work, this was the first cold night, I am unsure if the PTR heater ever worked
12/4 - Left at dealership
12/4 - Dealer said PTR heater broken, would be 1.5 weeks to get parts and fix
12/10 - Dealer said parts are on back order, would be delivered 12/23 or 12/24
12/10 - opened a complaint with Nissan consumer affairs
12/13 - Dealer now says parts will be delivered on 12/16 ( much quicker than the initial estimate of 12/23! )
12/16 - parts are at the dealership, new estimate is that it will be ready by 12/19. According to the dealer, this assembly has been redesigned. There is a new blower housing, duct work, clips, and other stuff I am not aware of. They are saying this is around 13 hours of work to take the dashboard apart, get parts swapped and back together. They said this is the first time they have done this procedure.
The dealership has been very helpful and I strongly recommend them, Nissan corporate not so much. The dealer has provided me with a loaner car. I have been told that I will be reimbursed for all gas, I am still talking with Nissan about other reimbursement.
For the first week, I did have some heat, but I suspect that was just the heat pump. Once temps got into the single digits on 12/3, my guess is that the heatpump did not come on, and the PTR heater was broken. I do think it is odd that the 2013 models have been out for so long and this design is still changing. Hopefully this will address the issue, I am not sure if Nissan will only be changing this assembly for owners that have problems, or if they will retrofit all PTR assemblies.
I will post a final update once I get the car back. If others are having this problem, I would recommend opening a case with nissan consumer affairs at 877 664 2738, once you get a case number, your local dealer can reference that and help you out as well.
Hope this helps others