Caroline, when are you traveling to Greece?
Since June 30 is the date the debt payment is due, it will be a key date.
News reports today, as you most likely also saw, are not encouraging. But, if Greece exits the euro zone, it would likely have larger implications for the country than problems with tourists being able get money (euros or other) out of ATMs.
If the negotiations are not resolved before June 30, and if you will (still) be traveling to Greece with a schedule that would have you in the country then, I'd probably wear an extra money belt with E1000 in 20/10s, as well as an equal amount of US dollars. Extreme? Well, there could (operative word....who knows?) be unusual issues with which to deal.
The Greek Tourism office in New York (Google) was especially helpful to us when we had a trip planned to Greece when the massive strikes were repeatedly in the news several years ago (including the truckers strike, which meant petrol, food, supplies, etc. were not moving), as we evaluated go/no-go for our trip a month or two later. That office had some good inside info on strike schedules and the general strike (scheduling) psychology of the Greeks. Greece was calm when we traveled.
One of the benefits of traveling is that one pays more attention to World News, not only when they are planning to visit a country, but years later after they have visited. We, for just a short period of time, get a glimpse that helps us, just a bit, to better understand the issues when we read/watch later.