U.S. President Barack Obama and Republican challenger Mitt Romney embarked Saturday on the final stretch of their long, grinding presidential campaign, making their closing arguments in the handful of battleground states that will decide the outcome of a race going down to the wire.

National opinion polls suggest the race for the popular vote in Tuesday's election is so close that only a statistically insignificant point or two separates the two rivals. Polls in the nine battleground states tightened after what was seen as a poor performance by Obama in the first presidential debate, on Oct. 3, and the race has stayed close since then.

Yet Republicans are quietly acknowledging that Romney had so far been unable to achieve the breakthroughs needed in such key swing states as Ohio, where polls show the Republican trailing by several percentage points. No Republican has ever been elected president without carrying Ohio.

That leaves Romney with the tougher path to reach the required 270 votes the U.S. electoral college. He must win more of the nine most-contested states that are not reliably Republican or Democratic: Ohio, Florida, Virginia, North Carolina, Colorado, Nevada, Wisconsin, Iowa and New Hampshire.

Both candidates are making mad dashes through those states in the final days of the campaign.

After attending a briefing Saturday in Washington at the government's disaster relief agency on the federal response to Hurricane Sandy, Obama took off on a hustings route through four states.

His itinerary had him heading from Ohio to Milwaukee, Wisconsin, and Dubuque, Iowa, and ending the day in Bristow, Virginia, where former president Bill Clinton joined him and gave a hoarse-voiced introductory speech in front of a packed crowd of 24,000 people.

On Sunday, Obama takes his campaign to New Hampshire, Florida, Colorado and then back to Ohio. His team planned larger events for this weekend aimed at drawing big crowds in battleground states.

Early hints at results

Romney began Saturday with a morning rally on the New Hampshire seacoast. He then headed to Iowa and planned two stops in Colorado later in the day. He shifted an original plan to campaign in Nevada on Sunday in favour of a schedule likely to bring him back to Iowa, Ohio, Pennsylvania and Virginia.

In New Hampshire, Romney faulted Obama for telling supporters a day earlier that voting would be their "best revenge"

'It is time we lead America to a better place.' —U.S. presidential candidate Mitt Romney 

"Vote for 'revenge?"' the Republican candidate asked, oozing incredulity. "Let me tell you what I'd like to tell you: Vote for love of country. It is time we lead America to a better place."

The Republican nominee sounded the same message in Iowa and released a TV ad carrying the same message.

Obama campaign spokesman Jennifer Psaki said the president's revenge comment was nothing more than a reminder that if voters think Romney's policies are "a bad deal for the middle class, then you have power, you can go to the voting booth and cast your ballot."

With Obama maintaining a slight lead in Ohio, the Romney campaign sought to make a last-minute play for Pennsylvania, a state that has traditionally voted Democratic. The Democratic candidate has won Pennsylvania in the last five presidential contests.

Obama won Pennsylvania by more than 10 percentage points in 2008; the latest polls in the state give him a four- to five-point margin. Romney will campaign in the Philadelphia suburbs on Sunday in what Republicans cast as a sign of strength. Democrats describe the move as an act of desperation, but the Obama campaign is carefully adding television spending in the state and are sending Clinton to campaign there Monday.

The final frenzy of campaigning comes in the wake of Superstorm Sandy, which has dominated much of the news coverage for the past several days as New York, New Jersey and Connecticut recover from the brunt of its force.

Friday offered an economic finale to the campaign with the release of October jobs reports that contained better than average economic news but gave both campaigns a talking point. Employers added a better-than-expected 171,000 jobs last month, but the jobless rate ticked up to 7.9 per cent from 7.8 per cent — mainly because more people jumped back into the search for work.

While Friday's jobs report was unlikely to affect the election outcome, it brought the economy back into the national conversation in a country still preoccupied with the devastation wrought by Superstorm Sandy on the U.S. East Coast.

Upbeat messages

After months of attack ads, the Obama and Romney campaigns both closed out their campaigns with some upbeat new messages while their allied independent groups continued on a largely negative note.

Romney's campaign was running an ad across the battleground states titled "Clear Path," which pulled clips from the third presidential debate where Romney laid out how his presidency would differ from Obama's.

In crucial early voting, Obama holds an apparent lead over Romney in several key states. But Obama's advantage isn't as big as the one he had over John McCain four years ago, giving Romney hope that he could make up that gap in Tuesday's election.

No votes will be counted until Election Day, but several battleground states are releasing the party affiliation of people who have voted early. So far, Democratic voters outnumber Republicans in Florida, Iowa, Nevada, North Carolina and Ohio. Republicans have the edge in Colorado.

On the last day of early voting in Florida, voters at some sites in Miami-Dade and Broward counties were waiting up to four hours to cast ballots. Democratic Senator Bill Nelson asked his state's Republican governor to extend early voting at least through Sunday, citing "an untold number of voters being turned away or becoming too discouraged to vote."

Under the U.S. system, the countrywide popular vote does not determine the winner. Romney and Obama are actually competing to win at least 270 electoral votes in state-by-state contests. Those electoral votes are apportioned to states based on a mix of population and representation in Congress.

About 27 million Americans already have cast ballots in early voting in 34 states and Washington, D.C.