Sit down, have a brewskie, and let's chew the fat.
The Inuit used to chew on pieces of whale blubber almost like chewing gum. The blubber took quite a while to dissolve, so it just sort of helped pass the time while they were doing something else.
Alternative: Sailors had to chew on salt pork when supplies were low, complaining about the poor food as they did. To chew the rag is based on chewing pieces of rag when the chewing tobacco had run out.