SEOUL, South Korea — The Group of 20 summit ended Friday with a declaration of broad principles but no commitment to immediate action, signaling that the United States will have to go it alone in dealing with its fragile economy and near-double digit unemployment.

In their final declaration, leaders of the world’s most powerful economies pledged to work together and to refrain from protectionism and competitive devaluation of currencies. They also agreed to take steps to promote growth in low-income countries.

But when it came to specifics, a U.S. proposal to set numerical limits on trade surpluses and deficits was rejected. Leaders of the world’s 20 biggest economies pledged only to develop “”indicative guidelines”” to assess imbalances in the first half of next year.

They also refused to endorse a U.S. effort to force China to raise the value of its currency.

“”Any sense of global solidarity looks to have been yesterday’s story,”” said Tim Condon, chief economist at ING Financial Markets in Singapore.

Essentially, that left the administration — along with American workers, families and businesses — to shoulder the challenge and the likely pain of trying to solve the nation’s economic problems on its own.

“”Obama is now in a position where he must be prepared to act unilaterally to reduce the trade deficit and to shore up U.S. industrial and technological competitiveness or risk losing not only the presidency in two years, but also the American dream,”” said Clyde Prestowitz, a former Reagan administration trade negotiator and now president of the Economic Strategy Institute in Washington.

There are several possible scenarios going forward.

One is that the exporting giants, including China, Germany, South Korea and Japan, could change their positions: If the U.S. economic growth remains low, unemployment high and incomes stagnant, consumers could cut back on their purchases of imported goods — a development that could hit the exporting nations hard because there is no alternative market right now to absorb their output.

If demand for their products drops, the leaders who humbled Obama in Seoul might decide it was in their interest to do more to bolster the U.S. economy.

Another possibility is that American consumers will return to their free-spending ways — as a recent surge in imports suggest they might. That will mean more credit card and other debt, as well as a potential for another financial crisis, unless consumers’ spending power also accelerated. With unemployment seemingly stuck near 10 percent and businesses guarding their profit margins, a hefty round of salary increases looks like a long shot.

A third possible scenario, and perhaps the most likely, is that the U.S. economy will continue to struggle, growing slowly in an atmosphere of high joblessness and belt-tightening for government and ordinary Americans alike.

Certainly there are things Obama and the federal government could do to brighten future prospects.

Many economists believe the United States could bolster its competitiveness in the global economy by investing more in research and education. But the benefits would be relatively long term and would take new federal spending.

Given the prospect for partisan gridlock between the White House and emboldened congressional Republicans, such spending seems unlikely.

Even without congressional approval, there are other tools Obama could use.

He could cite China as a currency manipulator, if Beijing doesn’t move more quickly in adjusting its undervalued yuan, setting in motion a process that could lead to sanctions. His administration could apply tariffs unilaterally on certain imports, or undertake a Buy American program, as Ohio has essentially done for government business.

But such actions are fraught with political as well as economic risks. As British Prime Minister David Cameron warned Thursday, they could lead to a dangerous return to what happened in the 1930s when trade barriers, currency wars and other selfish actions by countries prolonged the global depression.

Although nations now have the tools to reduce the intensity of the standoff, the possibility of a currency war “”absolutely”” remains, said Brazilian Finance Minister Guido Mantega upon the conclusion of the two-day summit.

Canada’s Prime Minister Stephen Harper expressed similar concern, saying, “”G-20 credibility does depend on showing results … we cannot get out of this with beggar-thy-neighbor policies.””

Obama sought to put an optimistic face on prospects for the future.

“”Sometimes I think naturally there’s an instinct to focus on the disagreements,”” the president said, when in fact “”in each of these successive summits we’ve actually made progress.””

He said there was not a lot of discussion about the Federal Reserve’s recent plan to pump $600 billion into the U.S. financial system — effectively printing billions of dollars to spur U.S. growth.

The move has been widely criticized by other countries as a tactic to suppress the value of the dollar to help American exporters compete, though currency and other policies in the leading exporting nations are also designed to help their own economies.

America’s large public debts and fiscal deficits also drew fire, especially with fiscally conservative nations such as Germany, which resisted U.S. pressure for high-saving nations to step up their consumption. Even stalwart American allies United Kingdom and Canada were reluctant to support stronger U.S. language in the declaration on rebalancing, given their own domestic commitments to fiscal restraint despite resistance from their people.

“”I think it was always clear that the G-20 would be able to do little concrete on the imbalances, and it has indeed kicked the problem down the road,”” said Raghuram Rajan, a University of Chicago finance professor and former chief economist at the International Monetary Fund, which the G-20 has enlisted to help assess economic imbalances.

“”The reality is that every large country will do what it thinks is best for its own agenda, and any help they offer one another will be indirect,”” Rajan said. “”In the medium term, these agendas could converge, but the medium term is too long for political comfort.””

“”Any sense of global solidarity looks to have been yesterday’s story,”” said Tim Condon, chief economist at ING Financial Markets in Singapore.