Set a budget for your grocery bill and stick to it. Even if you have to buy all generic, or find some cheap and huge recipes that you can eat off of for a few days.
Pinpoint what is necessary in your life and what is unnecessary. For example and to go with my above suggestion about the grocery bill: I love to cook and I love to cook solid comfort food. However, I have to divide this into necessary and unnecessary. My family needs to eat and they need a balanced diet... necessary. I like to cook super yummy and hearty food that satisfies the soul as well as the body...unnecessary. My family can survive very well on simpler and plainer food for a while as a part of an overall budgeting plan. Find cheaper ways to get your family the nutrients they need. Protein doesn't have to come from meat, carbs don't have to come from wheat products, frozen veggies are just as good as fresh and you can buy them in bulk if you have a big enough freezer and save money on them etc... Look into using potatos more in your cooking. They have so many nutrients in such a compact bundle. Cut back on snacky foods in your house. Just keep a few healthy (and more filling) snacks around like string cheese, carrot sticks, bagels and cream cheese etc.. No more fruit roll ups, chewey bars, sugary cereal etc... Kids can survive just fine on two healthy snacks per day between their meals. Buy cereal in bulk. My kids can't tell the difference between apple jacks and the store brand that comes in the huge bag for less money. Things like this really add up over time and you will notice that your grocery bill goes down by a pretty healthy amount each month.
Also, things like cutting back on the whole perfect-organic-whole-food-all-natural-cleaning-product etc. mom business will save you TONS of money. It's really amazing how much money we spend these days on following the latest health fads. Families were surviving just fine without all of those fancy, uber-researched, healthier and more expensive alternatives a few decades ago, I'm sure our families can survive the same right now, for at least a while in order to enhance the financial health of the family, which is almost as important as physical health. Don't go so far as to cut out prescription meds, but maybe see if there's a generic form that you could take instead, and I WOULD cut out the vitamins and supplements for now (they're SO expensive) unless you have someone in the family whose health will truly suffer without them, like an underweight child with an eating problem or something.
I'm not sure what your situation is like, I don't know if you work out of the house, or if you are a SAHM, but if you can find the time maybe you could be baking your own bread, rolls, hot dog buns etc. (a huge savings over time, especially if you are doing the whole "starter-dough" thing) and consider planting a garden and canning your own vegetables. It's an initial expense with a long term savings. It's a lot of work though and some people don't think it's worth it ultimately and for some it isn't. I'm going to be doing it, but not for that reason alone, I wouldn't do it just to save money since it's such a hassle. I'm also doing it as a school project for my children.
Teach your family to entertain themselves at home. There are a million ways for kids to entertain themselves at home, you just have give them the chance.
Also, turn off your cable/satellite service if you can do it without losing your internet. This is a huge savings. First, you're not paying that bill any longer. Second, your kids aren't begging for everything they see advertised on TV (and eventually wearing you down until you get it for them). Third, your kids learn how to be content with what they have and they're spending more time playing outside which is way better entertainment than running all over town to different activities (that cost money).
Anyways, I could go on all day, but you get the point. Just look around, separate what is necessary from what is not, and get started with the cutting back. Once you've cut everywhere you can, then form a budget based on what you are now spending for necessary things and stick to it. You'll find that you have a lot more extra money every month than you used to to put down on that debt snowball.