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.
Late Tuesday, Michelle Obama issued a message through Twitter thanking supporters: "I am so grateful to every one of you for your support and your prayers. -mo"
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.