The timing is particularly delicate for Obama, who travels to Europe and then Peru this week in a final foreign trip capped by a conference of the very foreign leaders who negotiated the Trans-Pacific Partnership.
Obama is fulfilling the commitment he made at the start of his presidency to attend the annual meeting of the Asia-Pacific Economic Cooperation forum, a demonstration of his commitment to "pivot" US policy toward Asia -- of which the TPP is the embodiment of his economic efforts.
The initiative to shore up US influence and secure job-creating economic ties with Pacific countries was painstakingly negotiated over several years with 11 other countries together comprising 40% of the world economy. The implications of its demise for US standing in Asia and its allies there could be profound.
Proponents saw the TPP as a multifaceted agreement knitting the US into the world's fastest-growing economies while setting US standards for trade, labor and the environment. It also served strategic and security goals of strengthening alliances against China's regional ambitions and North Korea's burgeoning nuclear program.
Those broad ambitions ran aground against the populist, anti-trade sentiment that swept the US election campaign amongst both Democrats like Vermont Sen. Bernie Sanders and Republicans.
Trump's hostility to trade deals -- a pillar of US engagement with Asia -- and his campaign proposals to change longstanding alliances there had already unnerved the region. Now, the TPP's dire prospects will further deepen questions about America's long-term commitment to Asia and reduce its economic clout there, Asian leaders and analysts said.
"For America's friends and partners, ratifying TPP is a litmus test of your credibility and seriousness of purpose," said Singapore Prime Minister Lee Hsien Loong during a visit to Washington this month.
Trump was clear about his stance on the pact. He offered more detail about his anti-trade stance during the campaign than almost any other issue, calling the TPP "another disaster done and pushed by special interests who want to rape our country."
Many Asian nations fear living in a region dominated by China and see America's presence as a counterbalance to Beijing's rising power. But without the deal, Lee and others have warned that US economic influence in the region is at risk of eroding and -- without a counterbalance -- China's power will only increase.
"Asian countries want America to be engaged," Lee said. "But we need to know that this engagement will be sustained, we need to know that agreements will be upheld, and that Asia can depend on America."
As a result, Trump's campaign suggestions that the US scale back the Asian security umbrella it's had in place since World War II and that South Korea and Japan do more to defend themselves rattled those allies badly.
Michael Green, a former top adviser on Asia to President George W. Bush, said Trump's comments about security ties were more worrying to Asian nations that his anti-TPP stance. The remarks "were so unnerving" that Asian allies "are just focusing on trying to establish some kind of broad normalcy and locking in commitments to the basics of the relationship," Green said.
The TPP also had security aims. Secretary of State John Kerry has issued warnings about the strategic fallout of abandoning TPP, calling the deal "a key way to gauge American engagement in the Asia Pacific" and warning of the "serious consequences" of rejecting it in terms of American security, values and leadership.
Rejecting TPP "would be a gigantic self-inflicted wound on our nation," he said in October at the Chicago Council on Global Affairs.
The US needs close Asian partnerships to face what might be its most serious threat in the coming years: North Korea's steadily progressing nuclear weapons program. Close cooperation between the US and its Asian allies will also be important to deal with China's increasingly aggressive claims to disputed territory in the South China Sea.
Those alliances would be damaged "by us turning our back on an agreement already reached prompted and promoted by us, led by us, which we then turn around and reverse and say, 'sorry, we didn't mean what we said,' " Kerry said.
Just a little more than a year ago, that argument was part of what boosted Obama's effort to get the trade deal through Congress. But popular sentiment has been moving against trade deals, with even Democratic presidential candidate Hillary Clinton opposing the TPP despite praising it as secretary of state.
Trump in particular struck a chord with his anti-trade rhetoric. The states that pushed him over the top to victory -- Pennsylvania, Ohio, Michigan, Wisconsin and North Carolina -- have all been upended by trade competition, and voters there believe that trade has cost them their jobs.
Senate Majority Leader Mitch McConnell told reporters last week the Senate would not act on the trade deal during the lame-duck session of Congress. House Speaker Paul Ryan has said the GOP does not have the votes to pass it in the House.
And Sen. Chuck Schumer, who will become the chamber's top Democrat in January, told labor leaders Thursday the deal would not be ratified, according to a source familiar with his remarks.
Wendy Cutler, a former acting deputy US trade representative and key negotiator of the deal, said that beyond the damage to US leadership, there are economic costs to cancelling the pact.
With the vast number of consumers who buy US goods live outside the country, she said, ripping up trade deals with five of the fastest growing nations in the world doesn't help generate growth or create jobs at home.
"Globalization is here to stay," said Cutler, who now runs the Asia Society Policy Institute's Washington office, speaking at a discussion hosted by Georgetown University Thursday. "No one can stop it."
Cutler hopes that Trump will come to realize the benefits TPP would bring both to the US economy and US power once he assumes office.
"It's easy on the campaign trail to criticize the achievements of the previous administration," she said. "But once you're in the White House, what seemed to be a black-and-white issue is now very complicated."
Green, the former Bush adviser, noted that Trump's frequent refrain on the campaign trail was not that that he opposed trade but that he would negotiate better deals. Given that, Green believes there could be hope for Trump to renegotiate the deal down the road, given the number of people in his party who are pro-trade.
"I think TPP is in a deep sleep," Green said, "but I don't think it's dead."