How Good do They Want It?
The range in app costs is huge, the StackOverflow link is a good one that I've read myself several times as we were developing. If they really want to compete with Groupon (but likely in a niche I assume), everything that you do will have to work 100%. Not 95% or 90% but 100% otherwise users just won't use it (Think about a photo sharing app that 95% of the time successfully uploads your photo...).
Most people that are quoting the price to develop a "Groupon" clone are quoting an initial Alpha release. It may function, but its not something that you're going to give to anyone but alpha testers. Things may "work" but do they work on every device under regular conditions?
Once you get your testers on there they'll tell you 50 things that just aren't right and you'll be tweaking things. So if it cost 1x to get to Alpha it might cost 3x to get to a Beta release because things just won't work "right" and certain problems are just hard to get to 100%.
I could easily see this being 1,000 plus hours of development and more for design, management, testing, etc. It helps if you can copy something exactly but you rarely can do that.