If We Won't Recognize Problems They Will Go Away
Trying to exit the euro area, or defaulting on its debt payments aren't realistic options, for reasons that I've already explained (follow the links if you don't remember).
One option would be to borrow from fiscally stronger EU governments, such as Germany and Holland. But as that is perceived as a bailout, and as that is very unpopular in Germany and Holland, the chances of that seems slim. The one remaining option would be to borrow from the IMF, like several other EU countries (Including Latvia, Romania and Hungary) have in fact already done recently.
It seems increasingly likely that Greece will in fact like Latvia, Romania and Hungary borrow from the IMF, but some in the ECB and other institutions oppose this because, to quote ECB executive board member Lorenzo Bini Smaghi "The image of the euro would be that of a currency that is able to survive only with the external support of an international organization"
I find it this argument to be completely absurd, as such a move really would have no link to the survival of the euro (because first of all ditching it was never an option for aforementioned reasons and secondly even in the extremely unlikely scenario that Greece and a few other countries would ditch it, it would still remain in more than 10 countries), and would instead simply be a way to lower Greek borrowing costs.
While it could perhaps be argued that the existence of the IMF is bad for sounder nations and should therefore be abolished, there is no economic reason for any country that could lower its borrowing cost by using it to abstain from doing so. And that is true whether or not it has an independent currency. And to abstain from doing so just to deny the obvious reality that Greece has a high cost of borrowing is just silly and absurd.