There are two things that I think need to be part of any realistic attempt to stabilize Europe
1. The ECB needs to print more money, some of the debt has to be inflated away
2. The risks of sovereign default for private bond holders needs to be reduced
And any solution cannot rely on
1. The continued cooperation of European Countries, because they can't get along
2. Amending the treaties, because that would take too long and would be impossible anyway
3. Asking governments for money, because they don't have it or won't give it
You need to find a way to raise funds without individually asking European countries for money. If you do, you're going to have the same problem that you always have when trying to raise money for public goods. Each would benefit if everyone chipped in, but there is an incredible incentive to defect and not chip in yourself. Contributors to the EFSF bear all the costs, but only gain some of the benefit of a stable Euro. Also, the EU doesn't have the power to tax or a treasury, like the Federal Government in the United States does. So it can't get money that way.
The ECB may not be able to ask or force European countries to give it euros, but what it can do is just print them. European countries need Euros to pay their creditors, and the ECB can make as many euros as it wants. The only tax it can do is an inflation tax.
What happens then is that value of Euros declines (inflation), and anyone who has anything denominated in Euros looses money. But this, at least, falls mostly on people and countries who have things. And reduces the actual debts of European countries because their debts are denominated in euros. This is how sovereign countries usually weasel out of their commitments, it should work here too.
Although this is kinda similar to defaulting, this should be preferred by bond holders. Inflation can usually be limited, so the bond holders only loose some of their value, rather than defaults where there is every incentive for the defaulting country to go big. Also, a weaker euro should make Europe more competitive, giving a boost to exports and reducing imports. The southern countries have needed a weaker currency for a long time now, but instead have been stuck with a strong currency that is more of a benefit for northern countries like Germany with a positive trade balance.
The problem is that the ECB is legally prohibited from giving money to governments to pay down their debts. What it can do, however, is give the euros to the IMF which can then give the euros to governments. The ECB has printed euros before to place in certain IMF vehicles, although nothing on this scale. As far as I know, the ECB doesn't actually have to ask anyone's permission to do this. And this solution doesn't involve the EU or it's member nations deciding anything or working together.
The IMF has a great deal of experience rescuing (successfully and unsuccessfully) troubled countries. It can give countries like Spain or Italy or Portugal euros in exchange for the kinds of long-term reforms that will help them pay back their debts. The IMF is also not another European country, and I think a little distance would be good for whoever is trying to figure out a solution to this whole mess. When the people in these rescued countries, who have to put up with austerity and labor market reforms and all sorts of other unpopular dictats from unelected technocrats, start protesting at least it won't be against each other. Because goodwill among Europeans is already in dangerously short supply right now. And everyone hates the IMF anyway.
