For sake of reference, Papa John's actual profit on a $16 pizza is ~72 cents. They could raise prices (which I don't doubt they will end up doing), but then you get into fewer pizzas sold due to higher prices, and speculative arguments. The issue really is

Let me repeat. The OWNER AND FOUNDER said that the pizza cost TO THE CONSUMER might go up around 20 cents. Those are HIS WORDS. Most of the other food chains that DIDN’T do lavish fundraisers for Romney have already started talking about this as simply part of their operating costs, like any other change in their cost to do business. 

If 20 cents a pizza causes the chain to collapse, well, then I can’t IMAGINE what they will do when fuel prices or beef prices or other charges go up, as they always do, and are always absorbed by the consumer in some way or another.