I may be willing to pay $3 for a latte from my favourite coffee shop... but you're damn right I'm going to vote yes on $1 coffee. Why wouldn't I? This is going to result in a lot of businesses needlessly offering discounts to existing customers for little discernible benefit. On top of this, it sheds no light on the effectiveness of pricing structures, since there's nothing in the system that encourages the discovery of pricing equilibrium.
I've spoken to a couple of business owners who have done Groupons - they see it as a marketing expense that seems to have greater returns than many traditional methods (coupons books, junk mail, etc). But Groupon works in a way that this idea does not: it gets new customers (whether or not they're good new customers is besides the point).