The reason I said they grew too fast is I experienced this myself in the late 90s. I was with a public company that did email marketing services. That sector has turned out to be a massively profitable business. ExactTarget just went public about 6 months ago, and I know a lot of other private players who are doing very well.
The company I was with failed because they bought into the "get big fast" meme that was driving consumer Internet companies. So they went on a acquisition spree, tried launching too many products when they should've just focused on their core, opened several international offices etc.
AND they were already public, so they had to deal with all the BS that comes with that.
The did all of this inside of two years. It was senseless. A company culture rarely scales that well.
And it turns out that in most B2B markets (except for commodities like bandwidth), you don't need to grow that fast. You need to grow in a way that makes your customers happy, yes, but you don't have to worry about everyone suddenly adopting a new competitor (i.e. switching from Yahoo to Google).
But when you have investors throwing money at you, it's easy to think that every decision you make is genius and that you can solve problems simply by throwing money at them.
So to my original point. I think Groupon has multiple strategic options, but it may take them 3-4 years to see them through and in the meantime they have to justify their valuation to angry investors every 90 days. This would not be necessary if they hadn't bought into the "get big fast" mantra.
However, I believe they do have lots of cash in the bank so they may still have time to turn it around. It will be painful and take years.