If I were you I'd go ahead with it. The financial crisis shouldn't cause that much trouble for tourists - or at least it hasn't yet.
Cash payments have always been preferred, but you can check with your hostel/hotel beforehand and see if they'll accept a credit card payment.
Keep an eye on the news and let us know how it went!
Always good to have some cash when traveling in any country. In Greece "Cash is King" is the rule, and has been the rule for years.
As of July 15 2015 - most places (pretty well all of them) that normally accept credit cards are doing so, As many have mentioned, you need cash in Greece at any time, as many more businesses do not take credit cards than other European countries, or will express a strong preference (including lower price versus higher price) for cash rather than card.
Petrol/Gas are open and fuel has been consistently available.
Restaurants and hotels have been serving meals normally.
Transport methods have been as available as they normally are in Greece.
If in Athens, Patra or Thessaloniki and people start assembling/congregating in any large square, in a way that suggests they are obviously not there just to take stroll, chat to friends or family, then move your evening's location to enjoy the local scene, elsewhere, unless you wish to participate in a demonstration or protest. By and large this is most of what you need to do to be cautious, add in common sense and you have 99% of what it takes to avoid the avoidable. That remaining 1% is the risk that exists everywhere in the world, yes, including "there"!
Enjoy one of the top 5 most hospitable countries in the world.