President Barack Obama and Republican challenger Mitt Romney were locked in a tight race with three critical battleground states too close to call on Tuesday as voters decided between two starkly different visions for the country.

Early vote-counting on Tuesday in Ohio, Virginia and Florida showed a deadlocked picture with Obama and Romney running neck-and-neck. Romney needs all three to navigate a narrow path to the presidency, while Obama can afford to lose one or two of them and still win a second term.

But Obama has been named the projected winner of key states Pennsylvania, Wisconsin, Iowa and New Hampshire, while Romney is projected to win North Carolina.

As results began to trickle in from eastern and southern states, the preliminary tally was largely as expected.

Early projections handed 250 electoral votes from 21 states to Obama, including California, New York, Pennsylvania, New Jersey, Wisconsin, Michigan, Illinois, Maryland, Massachusetts, New Hampshire and the District of Columbia.

Romney has taken 203 electoral votes from 23 states, including Texas, Louisiana, Kentucky, Indiana, South Carolina, Georgia, Oklahoma, Tennessee, Utah and Alabama.

Al Jazeera’s Alan Fisher, reporting from the Romney campaign gathering in Boston, Massachusetts, said: “They’re not going to admit defeat at this statge until they see the final polls. But it is slipping away. They realise things are not going their way.”

Our correspondent added: “They were saying that Ohio would be very close, but Mitt Romney has behind there for months. This is a man who has been running for president for six years, and it could end tonight in Boston.”

Some 120 million people rendered their judgment between the Democratic incumbent and Romney after a long and bitter presidential campaign that magnified the differences between Americans wanting to continue Obama’s approach to fixing the ailing economy and those who want to try a new path.

‘Spirited campaign’

There were scattered reports of irregularities across the country, particularly from voters who said they were asked to show identification while waiting in line. In Pennsylvania, a judge ordered Republicans to stop demanding identification from voters outside a polling station.

Voting machines also broke down in a number of polling stations. One man in Pennsylvania posted a video of a machine which did not let him vote for Obama, apparently a malfunction.

Romney voted on Tuesday morning near his home in Belmont, Massachusetts. From there he hit the campaign trail, a rarity for presidential candidates on Election Day. His campaign had events in Pennsylvania and the battleground state of Ohio.

Obama voted more than a week ago in his hometown of Chicago, part of a campaign to encourage his supporters to take advantage of early voting. About 30 million Americans had already voted, a record number.

“Governor Romney, congratulations on a spirited campaign,” he said to reporters on Tuesday morning. “We feel confident we’ve got the votes to win, but it’s going to depend ultimately on whether those votes turn out.”

His vice president, Joe Biden, cast his ballot in the early morning hours in his home state of Delaware. He traveled to Chicago in the afternoon to watch the results with Obama.

Tuesday’s vote capsped off a gruelling campaign that became the most expensive in history. Candidates and outside groups spent some $2.6bn on the presidential race alone.

Both candidates have spent the last few weeks barnstorming the handful of “swing states” which will decide the election. Obama made campaign stops on Monday in Wisconsin, Iowa and Ohio, while Romney visited New Hampshire, Florida, Ohio and Virginia.

Obama used his final campaign stop to remind voters of his accomplishments: the economy’s slow, steady recovery from recession; the rescue of the American auto industry; and the end of the war in Iraq.

“It’s not just a choice between two candidates and two parties. It’s a choice between two different visions for America,” he said.

Obama has not laid out a detailed agenda for his second term, and Romney has seized on that in his final speeches.

“His plan for the next four years is to take all the ideas from the first term – the stimulus, the borrowing, Obamacare, all the rest – and do them over again,” Romney said, referring to the president’s $787bn economic stimulus package and his health care reform.

“He calls that ‘Forward’. I call it ‘Forewarned’,” the former governor quipped.

Obama, the country’s first black president, seeks to avoid being relegated to a single term, something that has happened to only one of the previous four occupants of the White House.

Whichever candidate wins, a razor-thin margin might not bode well for the clear mandate needed to help break the partisan gridlock in Washington.

Polls positive for Obama

Al Jazeera’s Rosiland Jordan, reporting from Golden, Colorado, says voters there showed no signs of election fatigue.

“People are very energised, both Republicans and Democrats,” our correspondent said. “People take these issues very seriously and do their research.”

“We did see a lot of people arriving in the main courthouse in Jefferson County with several people getting out of each car.”

The last round of national polls heading into the vote were good news for the president. A Pew Research Center poll showed him leading Romney by three points, 48 per cent to 45 per cent. The same poll had them tied last week.

But the popular vote will not decide the outcome. States are apportioned a number of electoral votes based on their population, and the candidate who wins a majority – 270 – becomes president. And the final state polls showed the president leading in most of the crucial swing states.

Surveys in Ohio have had Obama leading by anywhere from three to five points. A victory there would mean Romney would have to win at least six of the remaining eight battleground states, which seems unlikely: Obama led every poll conducted in Iowa, New Hampshire, Nevada, Virginia and Wisconsin.

Romney’s lone bright spot was North Carolina, where he looked poised to win by a narrow margin.

The entire House of Representatives, the lower house of Congress, is also up for election, as is one-third of the Senate, the upper house.

Republicans are generally expected to keep control of the House, though polls show them losing some of their 50-seat majority. Democrats control the Senate by the narrowest of margins: They hold 51 seats in the 100-member body. Polls show them maintaining that majority, and perhaps picking up one or two extra seats.