Greece can't recover because its exports are too expensive. Devaluing the currency in which those exports are sold in order to spur exports doesn't solve the underlying problem, which is Greek productivity. Imagine that the German economy is a Prius and the Greek economy is a truck hauling a ton in a trailer behind it, and the Greek truck is complaining that it costs more in fuel than the German Prius to get from the same point A to the same point B. Devaluing the Greek currency is like making fuel cost less especially for the Greek truck with no change in cost for the German Prius; sure, if the fuel is cheap enough for the Greek truck then maybe the Greek truck will be price-competitive in getting you from A to B, but the real solution is "how do we get the Greek truck to first dump the ton it's hauling behind it and then how do we make it more fuel efficient".
In a single-currency market, it is the responsibility of strong players to shore up the economies of weak players, or risk popular discontent in the weaker economy and the democratic dissolution of the common currency. German politicians have paid lip service to this but have not really put German resources to use in building up the PIGS economies because such a policy is unpopular with the German voting public, which wants to see those resources stay in Germany and to the nearsighted benefit of German taxpayers. This is the real root of the Euro crisis. There were always going to be weaker players in the EU, and it doesn't matter if it's Greece, it could very easily have been some other country. The question is what do stronger players do.
The US doesn't suffer from this issue because, to use an oversimplified example, California voters aren't discontent with FEMA funds used in hurricane disaster recovery areas. Californians are Americans before they're Californians, by and large.