There's already a huge variety in what food actually costs - You can spend $50 for a single meal at a fancy resturant, or you can pay 18 cents for a package of raman noodles. There's also a huge price difference between generic non-brand foods, brand name foods, and "organic" or "natural" foods. Basically, it is currently possible more or less to get your food bill to fit your budget. You currently may not be able to get the things you want, but you'll be able to get enough to stay healthy.
However, unless the extra price in food goes specifically and directly to the poor (and not the grocers), artificially raising the price of groceries will likely only make the poor even hungrier, as they'll only be able to afford the cheapest of the cheap items. A diet of only the cheapest goods may also cause malnutrition.
In order make this idea work, you'd have to apply a specific "food tax" to fund food stamps for the poor. We already have enough taxes, in my humble opinion, and food stamps are already available to those below a specific income level.
Many food budgets are already stretched thin because of high gas and other living expenses, and raising the food bill per month may bump some people out of the the "making it but living paycheck to paycheck" and into the "poor" bracket. In essence, artificially raising food prices will make more people poor, not less.