I'm not sure I see the business opportunity here. For one, the Groupon business model has been universally panned here on HN. Furthermore, the grocery business is a notoriously low margin business (both for the stores and the brands). Even for the higher margin items in a grocery store, very few items are really unique. Most products in the grocery store compete either on branding or on price. Since group buying appeals to the price conscious consumers, the are unlikely to remain loyal when they have to buy your product at normal price.

Finally, coupons for items you buy in the grocery store are wide spread and been around for decades. One of the revolutions of Groupon was being a coupon distribution channel to get coupons to places you normally wouldn't.