Greece is out of money, and its current government and economic policies are not supportive of a lasting solution. All the money it's borrowed has been wasted, flushed down the statist drain, in order to support Greece and its citizens in a style they can't afford. What's happening now is like musical chairs: when the Greek music stops (coming soon), someone (e.g., the EU, ECB and IMF) is going to have to record the loss on their balance sheet. The question is not whether Greece will default, but how it will do it and who will pay the eventual price.
Meanwhile, despite the strong likelihood that Greece will not find a lasting solution in the coming days, financial markets are not displaying any signs of distress. To be sure, there is lots of worry out there, but markets are still quite liquid and functioning normally. This makes sense, because a Greek default is not an earth-shattering event that comes out of the blue. It's been a long time coming, and Greece is a very small cog in the global financial markets.
The chart above shows 2-yr swap spreads in the U.S. and Eurozone. At current levels, swap spreads are well with the zone of normality. As such, they are saying that financial markets are liquid, and systemic risk is low. If a Greek default were a serious threat the stability of the Eurozone financial system and economy, swap spreads would be much higher—like they were when the PIIGS crisis reached a peak in late 2011.
The chart above shows the Vix index, a barometer of the market's level of fear, uncertainty and doubt. It's jumped up from 12 to almost 20 in the past six days, and that's telling us that markets are worried that something might go wrong. But if this were a really serious worry, the Vix would be a lot higher than it is today.
Putting the two together, it's obvious that markets are nervous, but it's comforting that there is virtually no sign that an unpleasant resolution to the Greek crisis presents any threat to financial markets or even the Eurozone economy.
If anything, a painful resolution to the Greek crisis would be a reminder to other countries that unproductive economies with bloated and inefficient governments are unsustainable and ultimately very painful for everyone. The best solution for Greece would be to grow its way out of debt, by reducing the size of its government and adopting pro-growth economic policies.
UPDATE: I refer you to a good post of mine from several years ago: "Greek Myths." It discusses in more detail why a Greek default and/or a Grexit do not spell doom for either Greece or the Eurozone.