Jarrett, who was given personal responsibility by Obama of the first ever White House Office of Olympic, Paralympic and Youth Sport, said that the President and the First Lady Michelle Obama considered the Olympic Movement and the Games itself as vital to diplomacy.
Michelle Obama - born and raised in Chicago - flew in to lobby International Olympic Committee (IOC) members on Wednesday whilst the President, a resident of the city for almost 25 years, is due in on Friday morning for the presentation to the members which is scheduled for 0645 GMT.
"This (the bid and winning it) is very important to them," 52-year-old Jarrett told AFP.
"But not just for Chicago and the United States. This to them is about diplomacy and reaching out to the world.
"They are committed to diplomacy and bringing together diverse communities and what better way of achieving that than through the Olympic Games," added Jarrett who is one of three Special Advisors to the President.
Jarrett, Iranian-born but of American parentage, said that despite scepticism from members of other bids - they are up against Rio de Janeiro, Tokyo and Madrid - the Obama's were coming to Copenhagen out of respect for the electorate of 100-plus IOC members and the Olympic Movement itself.
"The President and the First Lady coming to Copenhagen shows their passion for the Olympic Movement," said Jarrett, who in 1991 when she was Deputy Chief of Staff to Chicago Mayor Richard M Daley persuaded Michelle Obama - then engaged to the future president - to leave a private law firm and join the city administration.
"It also shows how important they believe the IOC is in making diplomacy work. The Olympic Games is a wonderful symbol of diplomacy."
Jarrett, a divorcee with one daughter, said that the battle to win the 2016 Olympics was similar to electioneering in the Iowa caucuses during the election process for the Democratic nomination last year.
"It is similar to the Iowa caucuses. It is very retail," said Jarrett, who is one of the Obamas' closest confidantes.
"It is about meeting people one on one. The First Lady has the opportunity to make a compelling case for Chicago.
"The President will endeavour to do the same thing when he arrives on Friday. We are not taking a single vote for granted. We will work for each vote until the very last moment and we are through the finish line."
Jarrett said that Obama's vision of how he sees the IOC and the Olympic Games fitted in with his own domestic programme regarding leading sportsmen.
"He is a keen sportsman. He likes to play a bit of golf and basketball and is a red hot fan of the Chicago Whitesox baseball team.
"However, he wants to see sportsmen and women get more involved in community affairs. He did this with the Pittsburgh Steelers when they won the Super Bowl earlier this year.
"He -- as is usual with winners of major sports events -- invited them to the White House but instead of simply a reception and a photo opportunity got them to do a public service event.
"He got them to put together care packages for our wounded warriors.
"This is all part of his strategy of getting athletes involved in community work and giving back to the communities, and seeing there is a life outside sports."