Food stamps run out in March which generally sets a deadline to any shutdown. If it reaches that far the side that relies on the foodstamp vote will end up being forced to agree to practically anything. Even setting pragmatic politics aside, when the food stamps run out you're likely to see urban riots, looting, and so on that would rapidly force a the same concession in any case.

I would be extremely surprised if the shutdown reached February since the closer we get to the March, the more leverage this side loses.