Both President Obama and Mr. Romney campaigned in states they need to win in an election that opinion polls say is very close.

Mr. Romney told a boisterous rally in the state of Florida that he is the only candidate capable of bringing about change.

Both campaigns predicted the winner will be determined by which of their operations can get the most supporters to the polls.

In the state of Wisconsin, President Obama urged a crowd of cheering supporters to vote Tuesday.

U.S. presidential elections are not decided by the nationwide popular vote, but by an Electoral College system.  The importance of each state on the outcome of the election is approximately equivalent to its population. 

Both candidates campaigned in the critical state of Ohio on the eve of the election.

Larry Sabato is director of the Center for Politics at the University of Virginia.

“Ohio has been right 27 of the last 29 presidential elections," said Sabato. "It also is the key swing state this year because it is very difficult for Governor Romney to get to the magic number of 270 [needed to win] in the Electoral College if he does not carry Ohio’s 18 electoral votes. That is why there is such a giant battle there.”

Political polls say the race is very close nationally. But state-by-state surveys show Mr. Obama with narrow leads in many closely contested states likely to determine the outcome.

Analyst Larry Sabato said, “This is a close, competitive election, but the incumbent, President Obama, has an edge in the key swing states. Because it is close, however, you cannot absolutely rule out an upset by Governor Romney.”

Along with the race for president, all of the seats in the House of Representatives and a third of the 100 Senate seats are being contested.

Most analysts predict Republicans will continue to hold their majority in the House, while the president’s Democratic Party is likely to maintain a slim majority in the Senate.  

Millions of voters already have cast ballots under early-voting rules. 

But the vast majority of the electorate still will head to polling places throughout the U.S. Tuesday.