Obama is under pressure to push along stalled Mideast peace, prove the United States is serious about climate change and rally allies against the nuclear threats of Iran and North Korea. Restless leaders in Europe and elsewhere are pressing Obama to reform risky U.S. financial behavior and get Congress on board.
He also bears the load of two inherited wars that now bear his imprint - the one he's winding down in Iraq and the one that's widening in Afghanistan. Eight years after the Sept. 11 attacks, Obama must hold together international will as he tries to keep Afghanistan from becoming an al-Qaida launching pad again.
The talks have the potential to be galvanizing moments or opportunities lost.
"Leadership is not just telling people what you want, as the Bush administration discovered. Leadership is getting people to do what you need them to do," said Jon Alterman, a senior fellow in Middle East policy at the Center for Strategic and International Studies and a former State Department official in President George W. Bush's first term.
Obama will have his chances.
His first speech to the 192-member General Assembly will outline his view of leadership, emphasizing a new brand of cooperation as if to underline he is not Bush. As U.N. ambassador Susan Rice described the message: "Everybody has a responsibility. The U.S. is leading anew. And we are looking to others to join."
Obama will be the first U.S. president to be chairman of the Security Council, whose rotating presidency happens to be in U.S. hands this month during the annual meeting of the General Assembly. He expects to emerge from that special summit on arms control with a resolution that advances his goals of a nuclear-weapons free world.
The measure will try to put heat on Iran and North Korea without singling out any country.
With his domestic agenda consumed by health care, Obama is under pressure from world leaders to put more muscle into fighting climate change. He will seek to do just that this week, too, with a speech at a U.N. climate conference.
Time is short, though, for the U.S. to have leverage. An international conference is set for December in Denmark to a new global climate pact. Although the House has passed a bill to limit greenhouse gases, Senate action may fade until next year.
Perhaps as important as the speeches will be the conversations the world never sees.
Obama, who arrives in New York City on Monday for the annual U.N. gathering, will meet privately with the leaders of Russia, China and Japan. Less formal sessions will take place all week.
The showcase for the new U.S. president is getting familiar.
In just his first year, Obama has made it through summits with heads of both the world's 20 top economies and eight major industrial powers, as well as Western Hemisphere heads, Russian leaders and NATO. The president hasn't been shy about calling for the U.N. to take on "big, tough" problems more effectively.
When the focus shifts to Pittsburgh, Obama will run the Group of 20 summit of the rich and developing countries that represent 80 percent of world economic output. Although their united, expensive efforts earlier this year helped halt the economic slowdown, there is enormous work left and wide divisions about how to proceed.
"All of us need to act more responsibly on behalf of a better economic future," Obama said in a Saturday radio and Internet address that looked ahead to the G-20 summit and warned of complacency.
European leaders are frustrated about the lack of U.S. action on financial regulation and restricting how bank executives get paid. Just ahead of Obama's travels, details emerged of a Federal Reserve plan that would for the first time police how banks pay executives to minimize reckless investment gambles.
Obama himself is pushing Congress to get moving - he just went to Wall Street to say as much. But that effort is unlikely to satisfy his fellow leaders.
"You're hearing very strong concern that the lessons haven't been learned," said Heather Conley, who served in the Bush State Department and now runs the Europe Program at the CSIS think tank. She said Europeans fear a sense of urgency has been lost, and they are asking, "Americans, what are you doing about it?"
The events of just the past several days will influence Obama's agenda, too.
The president has penalized China over tires exported to U.S., citing trade rule violations. The move has infuriated an economic ally and stoked fears of further protectionism.
He just scuttled Bush-era plans for a missile defense system in Eastern Europe, swapping it for a more mobile system aimed at a changing threat from Iran. That change has pleased Russia, which Obama said had no reason to worry in the first place, while causing consternation in the region.
His Mideast envoy has failed to bridge gaps between Israelis and Palestinians, casting fresh doubt over peacemaking talks and the U.S. influence over them. That could dash any chance for an anticipated meeting in New York involving Obama, Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas.
And then there's the shadow of Iran.
President Mahmoud Ahmadinejad on Friday again questioned whether the Holocaust actually happened and asserted that Israel was created on "a lie and a mythical claim." That set an ominous tone for the U.N. - Ahmadinejad will be there - just as the United States and five other nations head toward an Oct. 1 conference with Iran.
Obama's biggest communications challenge may be to make sure his own message dominates.
That means, as Rice put it, trying to "bridge old divides and resist the efforts of a handful of customary spoilers."