Domestic Private Balance + Domestic Government Balance + Foreign Balance = 0
So what does this mean? Basically, gov't balance is the inverse of private balance plus foreign trade balance. If one area is paying out, another must be saving. So, if you're the US, forever running a trade deficit, then either private or gov't areas must be paying out...or both.
When individuals and companies run up debt, the nation can buy overseas to match. If foreign trade is balanced, like the UK has been of late, then if people are cutting back on debt the gov't MUST pony up to match -- there is no choice; it's not discretionary.
When you hear Germany saying that the rest of the EU should promote austerity and live like they do, they neglect that they have a positive balance of trade, so the can balance the sovereign budget and still have dollars going into private savings. This means Germany can say "you should all be like us", when really, for every outflow there is an inflow, so somebody else is paying out. The US is one such donor outside the EU, and Greece is one inside the EU.
The EU experiment is doomed, as Germany doesn't want to pay out (who wouldn't like to be in their place?), yet individual states can't run much debt, so once they hit limits then either people have to suck it up and borrow, or they have to stop buying. In a sovereign state, gov'ts can spend at any point, with the risk of devaluing their currency, at which point they can't buy much, but they can easily sell. Greece doesn't have that luxury, so they have to devalue in place, which means a deflationary pressure locally, with dropping wages and prices. Maybe they'll get to the point that Germans won't be able to help themselves and they'll at least go to Greece for vacations, and maybe buy up the country.
More later on this -- I'm still sorting out the details in my head, and I'm not sure I can articulate the finer nuances at all. How GDP factors into the picture is pretty important.
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