This paper attempts to quantify the maximum amount of debt that a government can sustain by itself, i.e., the limits to public indebtedness. Using a Dynamic General Equilibrium model where the government is fully characterized, we compute the steady state inverse relationship between the public debt to output ratio and the size of the government, measured as the total public expenditures to output ratio. This line is the budget constraint of a government in steady state. Calibration of the model for the Greek economy to fiscal targets reveals that, for the period just before the current recession, i.e. 2002-2006, the debt to GDP ratio was very close to the calculate limits wich depends dramatically on the interest rates. However, short after de financial crisis of 2008, sustained deficits drove the Greek economy to a point where the Greek Government crossed the debt limit where the country could only meet its debt obligations only if international investors where willing to lend. We conclude that the hight initial level of debts previous the crisis together with the rise in interest rates were the causes of the posterior debt crisis.