And this could hamper his efforts on the weightier issues.
Despite Obama's fabled charm and powers of persuasion, his in-person plea for Chicago to host the 2016 Summer Games fell flat. It was a hugely embarrassing defeat. His adopted hometown _ considered a front-runner heading into Friday's voting _ didn't just lose, it took last place, shocking nearly all by getting knocked out in the first round while the remaining three contenders moved on.
The defeat could soon be a distant memory, and may never be more than a quixotic-blip trip. But if, for whatever reason, bigger losses start piling up in Obama's corner, his performance in this case could be regarded as emblematic.
Obama tried to put the best face on his trip, saying upon his return to the White House, "One of the things that I think is most valuable about sports is that you can play a great game and still not win." He said he was proud of everyone's effort.
However, almost every aspect of his involvement this week in the Olympics quest recalls a strain of criticism that has been gaining ground on him:
_ He's trying to do too much at once.
The line is familiar by now: It's nuts for Obama to tackle the dismal economy, the overhaul of two wars, a remaking of the U.S. health care system and climate change all in one year, and with other difficult issues on the agenda as well.
He has achievements to be proud of in less than nine months in office. But with most of the bigger issues still in the air, voters _ even some in Obama's own Democratic Party _ are beginning to wonder whether he's someone who tries a lot but succeeds at little, and whether he has the sense to focus on the most important things. A jaunt across the Atlantic, and an extraordinarily expensive one at that, doesn't help.
_ He doesn't have what it takes to close a deal.
The why-Chicago-lost story has many contributors, with Obama's last-minute flight to Copenhagen for an emotional appeal probably among the least of them. Regardless, he is now tied inexorably to Chicago's defeat, and that verdict isn't good.
_ He is a celebrity, for sure, but is that always a good thing?
Remember how Republican John McCain tried to stoke doubts about Obama during last year's presidential campaign by calling him all flash and no pan? A bit of that is in play here, too, where some perceive Obama as arrogantly relying too much on his celebrity status and not enough on the nitty-gritty work of winning votes. For instance, some IOC members resented the fact that Obama blew into Copenhagen for just five hours, jetting back down the runway toward Washington hours before the result was even announced.
"It can be that some IOC members see it as a lack of respect," said former IOC member Kai Holm.
_ He's too casual with the use of his own time.
This White House has been drawing questions about its tendency to turn to Obama as its only closer, with not much of a bench. Other White Houses have been more judicious about deploying their most precious resource, the president _ doing so only when really needed, and usually only when they know they can win. This reduces the chances of overexposure reducing his effectiveness.
It might have been wiser to know more about the vote count before he boarded Air Force One. In hindsight, there was plenty of reason to doubt Chicago's chances.
_ He's junior varsity-league, still learning on the job.
The votes of IOC members are notoriously hard to count ahead of time. But so are those in the U.S. Capitol. Will Obama do as poorly predicting how health care votes are leaning in Congress, and make similarly ill-fate strategic decisions as that long and complicated debate unfolds through the fall?
Keep in mind: If Obama had not gone to Denmark and Chicago lost, he no doubt would have been blamed for not making an effort. He tried, as he often does, to thread the needle _ make the trip, but make it a quick one to deflect questions about taking time away from the pressing health care and Afghanistan debates.
Aides said the president viewed the trip as worth it, despite the painful outcome. "If you can't do more than one thing at a time," said spokesman Robert Gibbs, "the president wouldn't have gotten through the first day."
But the president risks seeing the pool of his easy doubters grow with each misstep, even these smaller ones.
EDITOR'S NOTE _ Jennifer Loven is AP White House Correspondent and has covered the White House for the AP since 2002. Julie Pace reported from Copenhagen.