IOC members settling into their hotel in Copenhagen on Wednesday told The Associated Press that Tokyo, Madrid, Rio de Janeiro and Chicago are all capable of hosting the Games and there is no clear favorite.
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Samih Moudallal, an IOC member since 1998, described Friday's vote as like choosing between "four sons or your brothers."
IOC Vice President Chiharu Igaya said "many" are undecided and will make their choice only after the final presentations Friday.
Willi Kaltschmitt, an IOC member for more than 20 years, said possibly half or more of his 105 colleagues remain undecided.
The contest between front-runners Chicago and Rio de Janeiro is thought to be very close, so personal appeals to IOC members from Mrs. Obama and Brazilian President Luiz Inacio Lula da Silva could prove decisive.
The other two bidding cities, Madrid and Tokyo, are thought to be trailing but have not given up. King Juan Carlos' arrival likely will bolster the Spanish capital's bid.
Japan's new prime minister, Yukio Hatoyama, is also awaited - although the Tokyo bid committee isn't yet saying when he will arrive.
Mrs. Obama planned to get right to work on trying to sway the vote Chicago's way.
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The first lady's welcoming party in Copenhagen was more like a stopover. She chatted with the ambassador, kissed Chicago Mayor Richard Daley on the cheek and gave her old friends quick hugs hello before climbing into the waiting SUV.
As head of Chicago's delegation - and her husband's representative until he arrives Friday - she plans to meet with as many IOC members as possible to try to persuade them to pick her hometown.
"That's the perspective I bring," Mrs. Obama said earlier this week, referring to her Chicago roots. "That's the voice that I'm most comfortable using. But in this case, it's probably helpful, particularly given the fact that so much of where the games are going to be held are sort of right in my backyard."
Silva arrives in the afternoon and is also expected to meet with IOC members.
IOC votes - by secret ballot over several rounds - can be highly unpredictable. Aside from the paramount questions of whether bidding cities' Olympic plans are technically and financially feasible, emotion, sentiment, geography, politics, self-interest and other factors also play a role.
Last-minute and high-powered lobbying can be important - as then-Prime Minister Tony Blair and his wife, Cherie, proved when London was vying for the 2012 Olympics. Blair traveled to Singapore ahead of the vote and spent two days lobbying IOC members, inviting them to his hotel suite for one-on-one meetings.
Chicago has torn a leaf from Blair's playbook: Obama adviser Valerie Jarrett met with him last week to solicit his advice and get tips on navigating the IOC voting process.
Ultimately, the biggest choice for the IOC's 106 members may be deciding what statement they want to send to the world.
Giving the Olympics to South America for the first time would be bold and, Rio argues, even transformational. IOC members acknowledge the appeal of taking the games to unchartered territory. Rio's plans are technically strong, too.
"Policy wise, the IOC has to decide if we're ready to go to a new continent," longtime IOC member Dick Pound said recently. "That's the biggest paradigm shift. Is the time right?"
Sending the games to Chicago, on the other hand, could perhaps prove more lucrative and safe. It is possible that in these precarious times of global recession, IOC members will find the familiarity of the United States - which last held the Olympics in 1996 in Atlanta - to be comforting.
Chicago also has emotional pull in the shape of President Barack Obama. Should he win a second term in office, a Chicago Games in 2016 could offer a celebratory and spectacular backdrop for his final year as the first black U.S. president.
Mr. Obama is coming in person to Copenhagen to try to secure the games for his adopted hometown. He will be here for a few hours on Friday - elevating the games to an issue of national importance but also exposing him to political risks.
On Friday, both Obamas will be part of Chicago's final presentation to IOC members.
"We're not going to sing together or anything," Mrs. Obama said recently, drawing laughs. "I don't know if I can elaborate any more without giving away too much of it. ... All I have are my stories, my experiences as a Chicagoan, as an American, as someone who believes deeply that health and fitness have got to play a greater role in the lives of our kids and our communities, and as someone who believes that the Olympic and Paralympic Games will be the best way to bring that message home."
The city receiving the fewest votes will be eliminated after each round Friday until one candidate secures a majority. The vote is expected to go the maximum three rounds.
Some members tend to vote out of sympathy in the first round, which can produce some surprises. The key to victory is picking up votes from the cities which go out.
If Tokyo were to go out in the first round, it is believed many of its votes would go to Chicago. If Madrid goes out, the consensus is they would go to Rio.