It seems clear that Greece is insolvent, and Ireland probably is too. Portugal is more of a borderline case, but it's becoming less so by the day. Angela Merkel is demanding austerity in exchange for a bail-out; well, the government just revised down expectations for the economy this year. It now says that Portugal's economy may shrink by 0.9% in 2011, where before it was expected to grow at a 0.2% pace. Austerity will likely slow the economy further, reducing Portugal's ability to pay its debts. And remember, the European Central Bank is about to raise interest rates.
There are several big problems to handle here, but one big one is obvious—Greece, Ireland, and Portugal are probably all busted. They simply can't meet their obligations. Their debt will almost certainly need to be restructured. The euro zone isn't excited about doing this now, partially because it's worried about its banks and partially because it's hoping it won't come to that. But default looks inevitable.
It's easy to say this from a distance, but Merkel and other European leaders have their heads in the sand. They don't want Greece, Ireland, or Portugal to default because that would mean big losses for banks in their own countries, which would then have to be bailed out. But they also don't want to directly bail out the insolvent countries, because voters wouldn't like that much. So they're kicking the can down the road with half measures and hoping that somehow things turn up. It's a recipe for stagnation at best and disaster at worst.