Once you understand sectoral balances [2], you realize that having a deficit tends to be beneficial. It is not clear how large this deficit has to be (and there are certainly times when a surplus makes sense, though those are very rare). It is clear that in the long run average you really need a budget deficit to have a well-functioning economy.
The reason behind that is actually fairly simple and comes from the sectoral balances, which state that the balances of all sectors in the economy have to add up to zero. So if the non-government sector has a surplus, the government sector must have a deficit, and vice versa.
Private actors like to hold monetary assets, i.e. savings, bonds, and so on. This means that somebody else must hold corresponding liabilities. Will the desire to hold liabilities balance the desire to hold assets within the private sector? This is unlikely at best. If there is no outside source of monetary assets, then those private actors who are successful at accumulating assets will force less successful private actors to go into debt until this debt is no longer sustainable.
The logical way out is for the government sector to provide the required monetary assets, which is only possible via a government deficit.
Even more so, given that nominal GDP will continue to rise by inflation + real growth of the economy, there must be a nominal government deficit. Otherwise, the value of private sector net assets must necessarily decrease over time relative to GDP, i.e. the private sector is squeezed out of its asset position. This wealth-squeezing is certainly going to be contractionary. [3]
Under the current institutional arrangement, an ongoing government deficit means increasing government debt [1]. However, unlike for private actors, there is no sustainability problem for a monetarily sovereign government (this is where your comparison with Greece breaks down - Greece is not monetarily sovereign).
If you are genuinely interested in the topic, you may want to read Bill Mitchell's Fiscal Sustainability 101 series, starting here: http://bilbo.economicoutlook.net/blog/?p=2905. His writing is not the most polished, but it's still probably the best analysis on the internet of what fiscal sustainability even means for a monetarily sovereign government.
[1] Alternative arrangements are possible, but unfortunately, they seem to be one of the taboos in our contemporary society.
[2] http://www.slideshare.net/MitchGreen/mmt-basics-you-cannot-c...
[3] The only way I see to reduce private sector assets without contractionary effects is to go to those assets directly, i.e. tax the wealthy. That does make sense for other reasons as well, such as the accumulation of wealth leading to accumulation of power mentioned in the article. However, taxing the wealthy is not something you can deduce from economics alone - there is always a choice.