Is the Euro really doomed?

Probably not. The "United States of Europe" people want a more tightly integrated EU. They can get this by setting up a European Common Bank empowered to borrow money on the credit of the EU and use it to bail out Greece. So they are using the Greek debt crisis to push their pet hobbyhorse. Turning the EU into a United States of Europe would turn a lot of lack luster Brussels bureaucrats into officials of something big and powerful. And so they talk up economic doomsday scenarios to scare people into putting up the money.
The holdup of this plan is the German taxpayers. They correctly observe that an EU bailout of Greece will be done with their tax money, and under the control of Eurocrats rather than reliable German government officials and they see no reason to pony up that kind of money.
So sooner or later the Greeks will run out of other people's money and default. This will be tough on some stupid banks in Europe who loaned the Greeks wads and wads of Euros. Those banks won't get their money back. Some of them will probably go out of business on account of the humungous loss. Those banks are talking to their governments, and to the ECB, and saying "oh please don't make us loose all that money. Save us." And so, the EU keeps doling out money to Greece, and the Greeks give most of it back to the banks.
When the Germans cut off the money, Greece will default, and tell all those banks "Tough luck". Ought to happen inside of 6 months.
Question: Is this the end of the Euro? Probably not. It will be tough on Greece who will have to cut spending down to whatever they can raise by taxation. Or, Greece can drop the Euro, start up their own currency, and cover their deficit by printing fresh money.
But the biggies, France and Germany, want to stick with the Euro and so they will. All the other smaller countries on the Euro like Belgium and Holland will stick to enjoy the benefits of doing business with the biggies without the hassle and risk of currency swaps.
If they let three of four of the stupider banks go out of business, it will improve the competitiveness of the entire continent. Having stupid banks pour valuable capital down Greek drains does bad things for your economic growth.