The eurozone economy grew only 0.9 percent last year, and coming into this year many analysts were concerned about the possibility of another recession.

But, "the latest economic data from the eurozone suggest that recovery may be at hand," ace economist Nouriel Roubini of New York University writes on Project Syndicate. "What is driving the upturn? What obstacles does it face? And what can be done to sustain it?"

Aggressive easing by the European Central Bank has helped spark the rebound, he says. The ECB is buying 60 billion euros ($65 billion) of bonds a month to jumpstart the economy. And the euro's drop to a 12-year low against the dollar has boosted exports.

"But a more robust and sustained recovery still faces many challenges. For starters, political risks could derail progress," Roubini writes. "Slow job creation and income growth may continue to fuel the populist backlash against austerity and reform," he says.

So what should Europe do to extend the recovery?

"Germany needs to adopt policies — fiscal stimulus, higher spending on infrastructure and public investment, and more rapid wage growth — that would boost domestic spending and reduce the country’s external surplus," Roubini says.

As for the U.S. economy, GDP growth decelerated to 2.2 percent in the fourth quarter from 5 percent in the third. And now economists expect a further slowdown for the first quarter.

CNBC Rapid Update, which provides a median of up to 11 analysts' forecasts for economic growth, fell 0.4 percentage point to 1.4 percent for the first quarter, after Monday's news that consumer spending rose only 0.1 percent in February.

Stephen Stanley of Amherst Pierpont Securities forecasts zero growth for the first quarter. "This is turning into a recurrence of last year's nightmare first quarter, when weather drove the GDP figure deep into negative territory," he wrote in a report obtained by CNBC.

The economy shrank 2.1 percent in the first quarter of last year before rebounding to post an expansion of 2.4 percent for the year as a whole.

Stanley and others anticipate a rebound this year too. Economists' median second-quarter projection is for growth of 3.5 percent, according to CNBC Rapid Update.

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