Berenberg's Schmieding thinks there's a 25 percent chance that Greece will leave the euro in the next six months, if its parliament balks at painful austerity measures and euro members are reluctant to provide more help. But he thinks a Greek departure would cause "only temporary damage." Other economists think it could break up the euro.
Another hotspot is Spain, the eurozone's fourth-largest economy. The country's debts are piling higher as its regional governments struggle and its economy shrinks. The ECB's offer two months ago to buy unlimited amounts of government bonds is a potential life-saver, but the country's Prime Minister Mariano Rajoy needs to formally request such aid. He has held off, apparently hoping the current market calm will last and he won't suffer the political humiliation of taking a bailout. Analysts say that if he waits too long Spain's borrowing costs could rise again to unsustainable levels and reignite broader fears in financial markets.
Banks are another problem. Weakened by massive losses on the government bonds they bought and real estate loans that aren't being repaid, banks across the eurozone have been propped up by governments that are themselves struggling financially. Even with the help, these banks have been forced to reduce lending, which has hurt Europe's economy.
A banking supervisor for all of Europe could provide some relief, by forcing crippled banks to merge with healthier ones. But it will be the second half of next year, at the earliest, before the supervisor is in place, banking analysts say. European leaders disagree over how much authority to give the supervisor and how to fund it.
Economic growth is what would ultimately end Europe's crisis. But robust growth remains far off. The European Union forecast Wednesday that the 17-nation eurozone economy would grow just 0.1 percent in 2013.
Privately, European officials say the ECB's bond-buying plan has afforded them a crucial window of opportunity — a year, perhaps — to resolve their biggest challenges.
Much depends, they say, on what gets accomplished in that time.