Greece cannot both stay in the Euro and sort out its debt crisis. The country has been living well beyond its means. It needs not only to cut expenditure and borrow less. It also needs to let its exchange rate fall to a more realistic level. It cannot do that inside the Euro.
In February we showed how Ireland could leave the Euro. The same approach would work for Greece. Here are the steps. It's not pretty, but it is more orderly than what could happen.
1) Announce you are leaving. (It would have been better to do this a while back, when it would have been a surprise, and before people started to pull their capital out of Greece.)
2) Denominate all Greek assets and liabilities in the 'Greek Euro' at a 1:1 initial rate. People continue to use Euro notes with the letter Y (for Greece) in the serial number. So cash machines still work. And Gresham's law means that non-Greek Euros will soon be driven out by Greek ones.
3) Announce that all your Euro debts are also now also denominated in Greek Euros at 1:1. You won't be able to maintain that exchange rate for long, but that's the idea. It will be your creditors who take the exchange risk hit, not you.
4) Default. It's inevitable anyway. Offer creditors (say) a 50% haircut, or a new bond maturing (say) 15 years from now. Hope that they take the 50% haircut. Sure, you won't be popular in the capital markets for a while. But if you can balance your budget you won't have to borrow anyway, and devaluation will help that happen. Investors will see you are doing the right things for the future, and will return sooner than you think.
5) You can print your own new currency and gradually exchange the Greek Euros for it. But don't tie your currency to any other. The whole idea is that you should have exchange rate flexibility, so that when another crisis hits, you can adjust.