Here's why Groupon works: data compression. A groupon is a signal compressing all of the economic data in an entire city into a single very best offer, at a rate of one per day. Consumers are overloaded with information and seek simplification, the value derived is a function of the ratio of compression.
Here's how Groupon can fail: they start offering more than one coupon per day. Anything that increases the perceived noise/signal ratio in crowded inboxes.