We've had our financial difficulties recently with a very limited food budget to feed our family of four.
I like things that can S-t-r-e-t-c-h. For example, a whole chicken, roasted is dinner and lunch for the four of us (mostly dark meat), the white meat is mixed with other stuff for another main meal(non-paleo DH and kids like homemade chicken pot pie, or in a tomato sauce with veggies that I eat on zoodles, and the rest of the family eats on pasta), and a BIG pot of bone broth from the carcass. That's several meals for our family of four from an inexpensive chicken, hopefully bought on sale. You can do the same this time of year with an inexpensive turkey and eat it for many, many meals (which is one reason I despise turkey because my mother did exactly this). I ferment my own vegies--a head of cabbage or beets when they are cheap go a long way. In the bounty of summer I dry veggies, fruit, and spices purchased ridiculously cheap in their seasons which I can use all the rest of the year. I try not to waste, so if I have leftover veggies, fruits, herbs, etc, I toss them in the dehydrator rather than throwing them away. They can always be added to soups and other dishes.
Last night I sauteed chicken livers--frozen ones are very inexpensive and these are great for you. I stock up when there's a sale. WF sells grass fed beef soup bones for cheap (usually $3 for a big bag) and the beef broth can appear in many meals.
I also never buy what I can make from scratch for cheaper. I make our yogurt (costs only as much as the milk) and kefir (get free grains from Freecycle). These homemade products can stand in for sour cream, cream cheese, etc. if you do dairy. We don't buy many packaged foods--ingredients are almost always cheaper and taste better when we make from scratch. Since my family isn't paleo, I bake some of the bread they eat. It costs me 50 to 80 cents to make a loaf of bread that costs $4 to $5 in the store.
Bulk bins are your friend, because you only need to buy exactly the amount you need, and you're not paying for packaging. So you can buy small amounts of paleo friendly ingredients to "garnish" dishes without breaking the bank. I buy a handful of macademias at a time this way--more would be way past my budget. An added bonus, assuming you buy at a store with good turnover, is that such bulk items are usually nice and fresh.
I'm not saying this doesn't take time and effort, but it's doable. I work full-time, so after dinner is my time for kitchen "projects" to feed the family. I like knowing that I can still feed my family healthful food in difficult times.