Mr Obama said he knows Romney supporters are "just as engaged, just as enthusiastic".
He spoke to reporters briefly after making calls to Wisconsin campaign volunteers from a campaign office near his Chicago home.
Mr Obama said he and first lady Michelle Obama were grateful to all of the campaign volunteers who have worked hard on his behalf. He was greeted by thunderous applause by about two dozen volunteers, many with tears streaming down their face.
During one call, he told a woman: "Hopefully we'll have a good day." And he told her to "keep working hard all the way through".
Earlier, Mr Obama's running mate, US vice president Joe Biden, cast his vote in the election, saying "it's always a kick".
He said it is the eighth time he has run for election state-wide. Asked if he thought it was the last time he would vote for himself, he told reporters: "No, I don't think so."
Also accompanying the vice president were his son, Delaware attorney general Beau Biden, his wife Hallie and their eight-year-old daughter Natalie.
Mr Biden shook hands with and hugged other voters as he waited. He urged Americans to vote "even if you have to stand in line".