Washington ? President Barack Obama left Asia with a greater foothold in the emerging nations that could help shape the American economy for years. But his failure to deliver on his own high expectations on key economic issues served notice that the global stage is not nearly his for the taking.

President Barack Obama boards Air Force One as he departs Tokyo, Japan, on Sunday.

The president returned to Washington on Sunday with mixed results to show from his longest foreign trip abroad as president, an exhausting 10-day tour through India, Indonesia, South Korea and Japan.

His first two stops yielded dramatic diplomatic successes and memorable images in two booming Asian democracies that will only become more important strategically to the U.S.

But the narrative soured once Obama arrived in Seoul, South Korea, for a meeting of the Group of 20 developed and emerging economies. Obama failed to achieve a free-trade deal with Korea that was to have been the biggest trophy of his trip, and instead of banding with America against China’s currency manipulation, several countries aligned themselves against the U.S.

Ups and downs

The trip ended anticlimactically in Yokohama, Japan, with an uneventful gathering of the Asia-Pacific Economic Cooperation forum. But Obama has no time to breathe easy. Almost as soon as he gets back to Washington he’ll have to grapple with combative Republican congressional leaders at a White House meeting, then head back overseas for a summit of the North Atlantic Treaty Organization.

“Overall, it was a mix of successes and deep disappointments,” Mike Green, senior adviser and Japan chair at the Center for Strategic and International Studies, said of the trip. “Two great visits in India and Indonesia, a real disappointment in Seoul, and a reassuring but curiously unambitious visit to Japan.”

Obama, in some ways, achieved what he set out to do.

By spending so much time in Asia, undeterred by his and his party’s midterm election “shellacking” on the way out the door, he showed key nations how important they are to the U.S. agenda. And that, in turn, is an investment he expects to pay off over time — by loosening up trade and hiring opportunities for his own constituents, and by building up the base of democratic and America-friendly voices in a fast-growing region of the world where communist China looms ever larger.

“I think all of Asia is eager for American engagement and leadership,” Obama told reporters on Air Force One on the way back to Washington. “Everywhere in Asia, what I heard from leaders and people is that we are still central, and they want us there.”

National security adviser Tom Donilon told reporters, “I think that the United States has dramatically advanced its critical goals and its strategic interest in the region.”

Highlighting problem areas

In essence, trips like this are down payments on diplomacy, even when immediate returns are neither as great as the president wants nor as measurable to a press corps holding him accountable for his soaring promises.

Yet the trip also underscored one of the president’s most nagging problems. He is operating in a world, particularly in regard to the economy, in which he takes a long view and voters want more immediate gratification. It is much harder for the unemployed, for example, to take much cheer in all the talk of the emerging international structure of the G-20. They want jobs and security now.

And so when Obama stood at the podium in Seoul with South Korea’s president and failed to announce the completion of a trade deal that would have been a breakthrough, it seemed to set the tone for the rest of the trip and colored the outcomes of the two economic summits that followed. The trade pact may still be finished within weeks, but its delay robbed Obama of a sense of flourish. It is never good for a president to be standing next to a world peer appearing empty-handed, and all the other cooperation Obama cemented in the course of the trip got overshadowed.

“The lone miscalculation appears to have been allowing the president of the United States and the president of South Korea to meet without an agreement on trade,” said Patrick M. Cronin, senior director of the Asia program at the Center for a New American Security. “In hindsight, an accord should have been hashed out months ago.”

Overall, the economies of Asia are “moving,” Obama said. “We should feel confident about our ability to compete, but we are going to have to step up our game.”

Some good moments

The best moments of the trips may have been during Obama’s three days in India, where he sealed $10 billion in commercial deals, firmly staking a claim in the booming country’s future prosperity, and delighted his hosts by announcing his support for a permanent Indian seat on the U.N. Security Council.

In Indonesia, Obama spoke to an appreciative, collegiate crowd in his boyhood home city in Jakarta, but the trip was brief — less than 24 hours on the ground, cut even shorter when ash spewed by a volcano threatened airspace. South Korea and Japan featured economic negotiations and meetings with world leaders including Germany’s Angela Merkel, Russia’s Dmitri Medvedev and China’s Hu Jintao.

The limits of America’s — and Obama’s — influence was on painful display as the G-20 failed to produce specific action against China’s currency undervaluation and Obama instead fielded questions about the wisdom of the Federal Reserve’s recent move to stimulate the U.S. economy through a $600 billion purchase of Treasury bonds, which is expected to inflate the value of the dollar.

Back in Washington countless challenges await: a lame-duck congressional session expected to feature a showdown over extending Bush-era tax cuts; negotiations with resurgent Republicans; and more potential shake-ups to the White House staff.

Despite all that, Obama left Asia on a personal high: a return visit to an enormous bronze Buddha statue in Kamakura, Japan, that he had seen once as a child. Just as he did as a boy, he even got some green tea ice cream.