You can! And it'll be better for you, or your baby and maybe both.
We have a family of five. On paper, in the Midwest, we are not destitute. Out household income is more than our average for our city. But, we are in a small urban, and we have many poor people. The thing that makes us feel like we're living paycheck is gas. And when it goes up, our pocketbook feels it. After paying for gas for the truck (an f-150 that commutes 80 miles per day), gas for my van (yay for getting a clinical site that is less than a mile from my house this semester, especially since I have to go the day before and then two days in a row!) and utilities, my cheap pay as you go phone, Internet/cable (most reimbursed by dh's job and that we can't just cut), school supplies, clothes (very minimal, we adore hand me downs!), meds for DH (30-80 per month, depending on I he needs his as needed med or not), copays, deductibles, household expenses, childcare and car maintenance, well often the only expense that can be cut is the grocery bill. I can coupon with the best of them, but most things I can coupon I can't eat!
So, what are my tricks? Buy in season produce. Buy from the side of the road by the local farm as this is cheapest, IMO! Try a farmer's market. Know your prices - keep a notebook if needed. For instance, in my area, Walmart has watermelons for $4.99 Giant Eagle for $5.99. Fenik's has them for $3.99 (when I was there last - this is a farm and prices may fluctuate), the stand in front of Wukie's furniture has them for $2.99. Can you guess where I've been getting watermelons? If you know your prices, you'll know whether a sale is good or not.
Another trick is to buy gift cards from Giant Eagle to places you are going to need something from (Home Depot, Walmart, etc) to earn fuelperks. They were running $.20 off per gallon for every $50 in gift cards, but I don't know if that is still going on. It's a great way to save on gas, but I need to get better at it! I do know what a good deal is, so I attempt to get those items there, which helps with fuelperks. I also am picky on meats and will only buy from Giant Eagle, Convenient or Fligner's. Fligner's is my favorite, but is the furthest, so we go there and stock up. They are pink slime free and I think all meats come from Ohio.
If you get WIC, if you shop at Giant Eagle, you'll get those fuelperks as well. When we were on WIC, even with my limited diet, the older two still needed milk and cereal and Rice Chex are covered! And as a breastfeeding mom you get a voucher for fresh fruits and veggies!
Check out grocery stores that you normally snub your nose at. Aldi's has a rep for a lot of heavily processed convenience food, but their fresh produce is good and cheap! Also, they often get organic foods in and organic foods tend to be more allergy friendly (not for every allergy, but I have found some that work with our list!).
Prepare to cook from scratch. Convenience foods just cost more.