the issue isn't one of not having their own currency.

http://en.wikipedia.org/wiki/Greek_government-debt_crisis

As a consequence of the unhealthy fiscal policy practiced during 2000–07, Greece was left with a twofold problem in 2008.

The first part of the problem was a too-high pre-existing debt level, leaving no room to absorb the increasing debts generated through a recession period without the market considering the debt pile would reach an unsustainable size, creating the so-called negative spiral of "interest rate death", which occurs if a country suffers from a constantly increasing debt that exceeds the sustainable level (at which the state is no longer forecast in the long run to be able to refinance or pay back its debt), which will mean the financial markets will start to ask higher and higher interest rates to cover the increasing risk for default. Higher interest rates will then cause an even more unsustainable debt-level, due to the increased government budget deficits stemming from increased interest payments, which will result in some still higher interest rates being required by the market; and the speed of this self-sustaining negative trend will likely keep accelerating until death occurs in form of a sovereign default, or alternatively trigger a situation where the government receive a sovereign bailout (with cheaper funding delivered by other sovereign states on favorable conditions through multiple years - as a last chance for the state to restructure its economy to enter into a more sustainable path).

The second part of the problem behind the accelerating debt-to-GDP ratio, also needing to be solved immediately, was the underlying fundamental problem of continued existence of way too high structural deficits of the government budget. Only starting from 2010, significant efforts and results were achieved in minimizing the structural deficits, through implementation of yearly packages with significant austerity measures.