I know HN has a libertarian, small-government bent, but there's a reason public spending is included in GDP: it's expansionary. The government pays people to do things, then those people buy things. This spurs growth. As with many things, it's a spectrum and going too far in either direction (austerity v. public ownership of economy) is a bad thing.
What is clear is that, when you have a quarter of your country out of work and fully half your future workforce untrained and non-contributing, you don't further reduce the consumptive power of your population. Unpopular an idea though it may be in these parts, Keynesian economics works in regards to recovering from recessions and depressions; disciples of the Austrian School have yet to show any ability to do so and their policies look set to spell the end of the Euro.
The private sector is fundamentally better and healthier in the long run for a nation's economy than its public counterpart, but when the private sector is depressed and getting worse through negative feedback loops, the public sector has to step in. It's the growth driver of last resort.