In Europe there has been a dramatic turnaround in how European countries like Germany and allies like Japan view the United States.

In 2008, under President George W. Bush, 31% of Germans had a favorable view of the United States. In 2012, under President Obama, 52% do. In Japan, in 2008, 50% had a positive view of America. Now, 72% do.

But in many Muslim countries Obama's policies have damaged views of the United States. In Pakistan, favorable views slipped from 19% in 2008 to 12% in 2012. In Egypt, favorable views decreased from 22% to 19%.

The biggest concern worldwide about America, according to the survey, still is that it acts without concern for the interests of other countries. But despite disappointment with Obama's policies, there is considerable support for his re-election, in Europe and in some Latin American countries like Brazil.

In France, 92% of those questioned think Obama should get another term. In Germany, 89% agree and in Brazil, 72% think he should be re-elected. In Mexico, however, 35% think he deserves another term and 43% oppose another term.

"Most of the publics in allied nations think he should be re-elected, and by large numbers," Kohut said. "If he had those numbers in the United States he could do really well!"

But in some Middle Eastern countries, it's the reverse. In Egypt, 76% don't want him to have another term and in Jordan, it is 73%.

Another finding in the survey: Even America's friends in Europe think China, not the United States, is the world's top economy.

As one man on the streets of London said: "If China sneezes, I think the rest of the world gets a cold."

But the Chinese themselves aren't so sure. Only 29% of Chinese in the Pew Survey said China is the world's leading economic power. Almost half said it is the United States.