After months of campaigning and billions of dollars spent in the battle for leadership of the world's most powerful country, millions of Americans arrived in what campaign officials for both Barack Obama and Mitt Romney are calling "strong" numbers at polling stations across the United States.

Speaking to the Washington D.C.-area newspaper The Hill, one Obama campaign official said early voting numbers were "good," highlighting high voting rates in Nevada, Iowa, Florida and North Carolina.

The unnamed source also indicated that there was a "strong turnout" in Columbus, Ohio, Dane County, Wis., and South Florida, all key in the battle for the so-called swing states en route to the White House.

“No matter what you hear ... about turnout in Republican counties or exit polls, particularly early in the day, it’s important to remember that, because of early votes, we’ve banked hundreds of thousands of votes already,” another Obama aide told The Hill.

On the Republican side, The Hill cited the Romney campaign as saying that a significant voter turnout could help the former Massachusetts governor win the more hotly disputed states.

“With a strong ground game in the states and momentum on our side, we are confident we will win this election,” campaign spokeswoman Amanda Henneberg told The Hill.

In addition, the New York Times reported that contested districts in Wisconsin, Virginia, and Florida were also reporting long lines at polling stations.

Both campaigns say the winner will be determined by which campaign is better at getting its supporters to the polls. The president needs the overwhelming support of blacks and Hispanics to counter Romney's big lead among white males.

"I encourage you to stand in line as long as you have to," Vice President Joe Biden told television cameras at a polling place in his home state of Delaware, where he and his wife were among the first voters.

Election Day turnout was heavy in several storm-ravaged areas in New York and New Jersey, with many voters expressing relief and even elation at being able to vote at all, considering the devastation from Superstorm Sandy.