The Frannie approach means a fiscal union: their debts are our debts. The AIG approach is the current “tough it out” one, where the hoped-for outcome is that a solvency crisis can be solved with liberal applications of government liquidity. But that only happens when you have strong growth—share-price growth in the case of AIG, with lots of expected future profitability, or economic growth in the case of countries like Greece, Portugal, and Ireland. And right now it’s impossible to see how a country like Greece can possibly grow its way out of its debt trap.
Finally, there’s the GM approach: restructure the debt, and get back onto a long-term sustainable footing. It’s harder for countries than it is for companies. But it might well be the least-bad option, by some large margin.