"Election Day is almost over," Obama said in a web video. "We won't get another chance tomorrow."
Obama aides appeared relaxed and positive and said their internal numbers had them on track for victory. But advisers said they weren't optimistic about Florida and North Carolina, two states that Obama won in 2008.
Still, Obama doesn't need victories in those states to reach the required 270 Electoral College votes.
The president decamped to his home on Chicago's South Side to watch the election returns with his family. He was expected to join top advisers at a downtown hotel later in the night.
Despite their outward confidence, Obama and his aides were leaving nothing to chance. The president indulged his superstitions by engaging in a traditional Election Day basketball game with friends, as the race that will determine his political future was finally in the hands of voters.
Obama's team won, ensuring him at least one victory Tuesday.
The president kicked off Election Day with a surprise visit to a campaign office near his South Side home.
Thunderous applause from about two dozen volunteers, many with tears streaming down their faces, greeted Obama. Removing his suit coat, he sat down to make some calls to volunteers in neighboring Wisconsin. "Let's get busy," he said.
"Hopefully we'll have a good day," he said on one call. "Keep working hard all the way through."
Speaking to reporters afterward, Obama said: "We feel confident we've got the votes to win but it's going to depend ultimately on whether these votes turn out."
The president also congratulated his Republican rival Mitt Romney on running "spirited campaign", saying he knew the GOP nominee's supporters were "just as engaged, just as enthusiastic" as his own.
The president headed into Election Day locked in a close race with Romney, according to national polls. But he appeared to have a slight edge in some key battlegrounds that will decide the contest, including Ohio, Iowa and Wisconsin.
Obama said late Tuesday in an interview with Denver television station KDVR that he had prepared both a victory speech and a concession speech for election night.
"You always have two speeches prepared because you can't take anything for granted," Obama said. Romney on Tuesday told reporters he has only prepared a victory speech.
There was no traditional Election Day photo of Obama voting Tuesday because he did so in Chicago last week, part of his campaign's effort to promote early voting. First lady Michelle Obama voted by absentee ballot.
One tradition Obama kept, however, was his Election Day basketball game.
A savvy basketball fan, Obama was joined by former Chicago Bulls star Scottie Pippen, childhood friends Mike Ramos and Marty Nesbitt, and Education Secretary Arne Duncan, a former captain of Harvard's basketball team.
Others who played included Obama's chef Sam Kass, first lady Michelle Obama's brother Craig Robinson, former Bulls player Jeff Sanders, and Alexi Giannoulias, the former Illinois state treasurer and 2010 Democratic U.S. Senate nominee.
Giannoulias said Obama was player-coach of his team, which included Giannoulias and Pippen. The game had referees and the teams played 12-minute quarters. Duncan and Nesbitt played on the other team.
In 2008, Obama played basketball with aides before winning the kickoff Iowa caucuses. They decided to make the games an Election Day tradition after he lost the next contest, the New Hampshire primary, on a day when they didn't hit the court.
"We made the mistake of not playing basketball once. I can assure you we will not repeat that," said Robert Gibbs, a longtime Obama aide who accompanied the president in the campaign's waning days.
The president's daughters, Malia and Sasha, arrived in Chicago after school Tuesday with their grandmother. The president's sister and her family were also joining the Obamas in Chicago.
He was expected to speak at his campaign's election night party at McCormick Place convention center.