"The risk is that complacency takes hold because there is no more urgency in the crisis, and that everything that has been done up until now will be deemed sufficient," The New York Times quoted Peterson Institute for International Economics senior fellow Jacob Kirkegaard as saying.
"Europe will turn into the next Japan, and become a permanently depressed or stagnating economic area," he said.
The effort to integrate financial systems in Europe should not be over yet, Harvard University economist Kenneth Rogoff told Monday's Times.
"They need to integrate more fully, or they will fall apart," he said.
Rogoff also said complacency was an issue.
"Some European policy makers who visited the United States recently were delighted to see that because of the 'fiscal cliff,' Europe wasn't on every [news] channel," Rogoff said.
"There is an ecstasy over the fact that they won't blow apart tomorrow," he added.
On the plus side, panic in Europe over the demise of the eurozone has largely evaporated. European Central Bank President Mario Draghi calmed the bond market by saying the ECB would do whatever was needed to support the euro. That lowered yields on bonds in Italy and Spain that were considered unsustainable.
Although the economy in Greece has yet to pick up steam, talks of Greece being forced to leave the eurozone have calmed down while talk of Germany leaving the eurozone because the region was holding it back also has quieted considerably, the Times said.
Fixing the financial system may be only half the problem. After that, the European economy must also move forward, economists said.
But there are some tricky turns in the road ahead.
In Germany, elections will take place in September that could displace Chancellor Angela Merkel, who has been given much of the credit as the architect of the rescue efforts so far.
Merkel has managed to keep the focus of the rescue on fiscal discipline and has been walking a tight line by trying not to inflame passions among German taxpayers who have largely foot the bill for the rescue.
Italians are also headed to the polls this year. In France, President Francois Hollande is struggling to meet economic goals. In Britain, Prime Minister David Cameron was to deliver a speech last week that said, "The danger is that Europe will fail and that the British people will drift toward the exit." The speech was postponed, however, by the Algerian hostage crisis.