If people have a bad experience with the Groupon at your store, the store gets inflicted with tons of bad reviews due to long lines, long checkout times, etc etc etc. While in theory this sounds like a good problem to have, its not and won't provide a sustainable stream of customers (i.e. majority of these customers come once, have an awful experience because of the aforementioned problems and never come back).
While my sample size is small (~15 biz owners) I saw it first hand at a restaurant in Somerville. My buddies and I stayed for 3 table turns around us. I overheard everyone that was there because of Groupon and every single table had no intention of coming back. They didn't mention the cause, but I am assuming it was slow service because the place had a 1.5 hr wait (normally 15mins).