I think that it is very possible. I have 2 adults and 6 kids and we spend about $300/ month on groceries in Canada. Soap, diapers and other non groceries are extra though.

We eat mostly all natural food, no prepacked lowcarb bars or shakes.

We eat plenty of meat, because I have a large family I buy the bulk packages of meat which is also less expensive per pound. The meat is probably at least half of the budget. When the Christmas turkey's are on sale I buy a few of them and freeze them. We can eat an entire turkey in one sitting with no leftovers!

We rarely eat out, because we have 6 kids it is at least $40 even at Mcdonalds.

The kids snack on fruit, vegetables and cheese. Nothing fancy and they do fine, as do I.

I am the only one low carbing, but because I am the one cooking I think that I am gradually reducing everyone's carbs, which in my opinion is cheaper.

I buy the artificial sweetener, which I rarely use because I no longer crave sweets. It cost me $3.99 and lasts me about 3-4 weeks. The $3.99 does not affect my budget enough to worry about.