Default of any country is not an option because of the inter-linkages. They either stand or fail together. A sovereign debt default will mean govts will have to bailout the banks holding the debt unless they are willing to see the banking system collapse. So they are better off monetizing the debt. Another approach is for the ECB to guarantee the debt if the countries are willing to accept certain fiscal conditions laid out ....meaning they will monetise it only when countries can't service it...that will buy plenty of time.
Given the size of the debt, there aren't many ways to solve this.