The government is spending substantially more than it collects in taxes, even before interest (primary budget deficit). In effect, they need to borrow to pay interest at current spending levels. Meaning that the debt will grow even faster unless they severely cut spending. The street protests indicate they may not.
A default could lead to contagion, surging interest rates and a loss of confidence in bonds. Capital would withdraw and that could lead to a Euro crisis.
The politicians know the ECB has a strong incentive to prevent this. The ECB knows the politicians know.