People in rural areas can grow food, but agricultural specialization means that many areas would have to shift from cash crops to more general production. A lot of rural areas in the west aren’t really suited for agriculture. Rural populations in the US are smaller than urban/suburban ones, and in some parts of the country the suburbs wouldn’t automatically be on the same side as the further countryside. So it wouldn’t be as easy to take on the cities as many seem to think.
My view is that the cities would take on themselves; I would expect a total civil breakdown in the event that there is a shortage of food or the heat and electricity shuts off. This ain’t London in 1940, Paris in 1914 or Vicksburg in 1863. I would imagine there would be little tolerance for discomfort of any type in the modern urban areas and the wealthy would be the most intolerant - can’t imagine the ladies of the Upper East Side New York doing required manual labor of any type. I hope none of this ever happens; it would be horrible.