There is only one institution with the resources to save the eurozone, and that is the central bank. Only a central bank has unlimited resources in domestic currency. Yes, the ESM can be granted a banking license and then borrow without limit from the ECB if you are looking for a clever end-run around the ECB's charter, but that's a gimmick. Either way, it's the ECB's money.
The eurozone can be saved with the combination of 5-6% nominal growth plus yield-targeting for eurozone government bonds. The ECB can target 5-6% nominal growth by engaging in asset purchases until such a growth level is reached. This would allow most eurozone governments to balance their budgets (if they so choose). The ECB can also set yield ceilings for the bonds of compliant governments, such that their current level of indebtedness can be made sustainable and thus, et voila, no more crisis. Thus, all of the PIIGS except Greece could be saved. (Greece can't be saved except by outright philanthropy.) As I have explained before, if yield-targeting results in excess money-creation, this can be sterilized by the issuance of "ECB bonds".
The consequences of these two operations would be above-target inflation (which is desired) and a substantial decline in the asset-quality of the ECB's balance sheet. The ECB would be directly exposed to the creditworthiness of its member governments, some of which are already below investment grade.
Let us assume that, by taking on these credit risks, the ECB's solvency is threatened. Although central banks do not mark to market, they are exposed to delinquency and default, as well as outright repudiation, as will occur in Greece. This is, we are told, why the ECB cannot rescue the PIIGS: because it will endanger its solvency and "credibility". Should the EU lose credibility, the euro will lose credibility as well. However, none of this is, in fact, true.
Many German commentators (and officials) have used the ECB's solvency as a rationale to oppose fiscal monetization. This is always stated as a truism without a shred of evidence adduced in its favor.
Central bank solvency is meaningless. In granting the central bank the monopoly of the issuance of fiat (paper) money, the government has granted it a license of inestimable value, the license to print money. The value of this license is not capitalized on the central bank's balance sheet. Like the value of the Coca-Cola brand, it is an uncapitalized intangible (not even footnoted). Thus, should a central bank happen to write down its assets by an amount greater than its capital, precisely nothing has happened because it can still print money. Does the Fed have a unit that performs the credit analysis of its principal foreign counterparts? No.
This would not be true, however, of central banks that make promises in commodities they cannot print, such as gold or foreign currency. Under those conditions, an analysis of their "cover" ratios is warranted. But if the bank is only printing its own liabilities, its resources are as irrelevant as they are unlimited.
Therefore, those who promote the falsehood that central bank solvency is necessary to the bank's credibility, are using mythmaking to promote a different agenda. If the eurozone is to be saved, the ECB's solvency can be sacrificed without consequences.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.