They aren't running up more debt. They've had a primary surplus since 2013, the problem is in the ECB/Euro system they have no way of reducing the external debt (i.e. let the relative value of your currency drop) to bring thier flows in sync with where they should be.
The only thing that will relieve them is for Northern Europe to increase thier inflation or to have the debts forgiven. That isn't politically possible due to internal politics in Germany, France, etc. So they're forcing the issue to end the "beatings will continue until moral improves" that is currently foisted upon them.