It not being the answer is good and fine but what I am missing is how not-austerity and pouring money into an overweight public sector that's been treating loans as income for decades is supposed to work without drastic measures from within. It seems doubtful to me that there is a basis to which growth measures could even be applied in a way that wouldn't just be more of the same that lead us here in the first place. I am not an economist.
I also find it doubtful how useful of a measure GDP is in the case of Greece where 40% of it is public sector.
When you pay someone's wages, you keep consumption up. If I get paid £20,000 by the government, I'll probably put £4000 of that in savings, and spend £16,000 on various different products. When you spend money on products, it then goes towards the various people involved - labourers involved in the construction of the product, the owners of the company, the supplier whose raw materials were bought. Each of them will also save some, and then spend, say £12,000. The cycle repeats. So, an income of £20,000 actually has a much bigger effect for the economy as a whole than £20,000. If you fire me, I lose £20,000, and then all of the products I would have bought don't get bought, so all of those people are worse off by £16,000, and all the people they would have bought from are worse off by £12,000, and so on. One man's expenditure is another man's income.
So, Greece is in the situation where by cutting public expenditure, it is devastating private economy. All of those public sector workers that went out to buy private sector goods don't buy them any more. That means that private sector firms suffer too, and reduce the wages they pay, and even make people unemployed - and the government then has to support those people with unemployment benefits, which means that by cutting public sector wages you don't actually reduce the budget deficit that much because you then have to support a lot more people on the dole.
There are ways out of this. When an economy is growing very rapidly, you can maintain public sector wages at the same level, but because the economy is growing, people not in the public sector do earn more, so the government has more tax revenue but the same expenditure, so it trends towards a smaller deficit or even a surplus without having a dramatic effect on the economy. The trouble is that is relies on having an economy that is growing very rapidly. Greece doesn't have an economy that is growing rapidly, because there's no investment. There's no investment because nobody is buying things in Greece, because they don't have money. One of the reasons they don't have money is that public sector employees have been cut by almost a half and the wages of the remainder dropped massively, so there are no consumers with the spare money to buy products in the first place.
So, Greece is damned if it does, damned if it doesn't. Every time it implements a reform to help reduce government expenditure, it damages the economy further, which means there is less government tax revenue, which means it has to reduce government expenditure again, which damages the economy again.
The solution, to the extent there is one, is to ride out the economic downtimes, and then implement reforms. I.e., increase government spending - run deficts of 5%, 10% - until the economy begins to recover, then slowly start reducing government spending and implementing reforms at roughly the same pace that the economy recovers. Greece can't do this because other countries won't let it. Obviously, Greece needs to undergo reforms anyway, but you can't implement reforms when you're in the situation Greece is in. It's like trying to replace the wing of an airplane you're flying in.
Public sector spending is also an important a part of GDP as anything else, for the reasons at the top. GDP is just Gross Domestic Production, and really is a bit of a misnomer because really, in the modern era (it's an old term), people normally mean Gross Domestic Output - we don't exclude the services sector from GDP after all, and they don't 'produce' things.