WASHINGTON -- President Barack Obama and Republican rival Mitt Romney attacked one another Sunday in frenzied campaigning two days before the presidential election, closing out what has been one of the most negative races for the White House in recent memory. Polling showed the candidates in a virtual tie for the popular vote nationwide, with Obama holding a slight lead in the all-important battleground states that will decide the outcome.

Beyond the nine so-called swing states, Romney was making a last-minute play for traditionally Democratic Pennsylvania with a massive advertising foray and a campaign appearance with running mate Paul Ryan in the state late Sunday, his first stop there this fall.

The Republican ticket cast the late push into Pennsylvania as a sign that Romney had momentum and a chance to pull away states that Obama's campaign assumed it would win handily. Obama senior adviser David Plouffe told ABC television Sunday that Romney's move was "a desperate ploy at the end of a campaign," given the Democrats' million-voter registration advantage in Pennsylvania.

Nevertheless, Obama was responding by dispatching deeply popular former President Bill Clinton to the state for a four-city sweep through Pennsylvania on Monday.

In heavily Democratic Cleveland, Ohio, on Sunday afternoon, Romney slammed Obama for what he termed the president's failure to end the partisan gridlock that has brought Washington to a virtual legislative impasse and for breaking his promises to vastly improve the economy while cutting the national debt.

"Talk is cheap," Romney said in the Lake Erie industrial city. "But let's look at the record." He went on to lash the president for what Republicans claim are a series of broken Obama promises on both the economy and changing the political climate in the country.

Regardless, national opinion polls showed the race for the popular vote in Tuesday's election so close that only a statistically insignificant point or two separated the two rivals.

The final national NBC/Wall Street Journal Poll showed Obama getting the support of 48 per cent of likely voters, while Romney receives 47 per cent. The poll had a margin of error of 2.55 percentage points.

A new national poll from the Pew Research Center found Obama with a three-point edge over Romney, 48 per cent to 45 per cent among likely voters, an improved showing indicating that the president may have benefited from his handling of the response to Superstorm Sandy. That poll had a margin of error of 2.2 percentage points.

The majority of polls in the battleground states -- especially in the Midwestern states of Iowa, Wisconsin and Ohio -- showed Obama with a slight advantage, giving him an easier path to the 270 electoral votes needed for victory. No Republican has won the White House without carrying Ohio.

Under the U.S. system, the winner is not determined by the nationwide popular vote but in state-by-state contests, making "battleground" states that are neither consistently Republican nor Democratic extremely important in such a tight race. Romney and Obama are actually competing to win at least 270 electoral votes. The electoral votes are apportioned to states based on a mix of population and representation in Congress.

That raises the possibility of a replay of the 2000 election when Republican George W. Bush won the presidency with an electoral vote majority, while Democrat Al Gore had a narrow lead in the nationwide popular vote.

If the election were held now, an Associated Press analysis found that Obama would be all but assured of 249 electoral votes, by carrying 19 states that are solidly Democratic or leaning his way -- Iowa, Nevada and Pennsylvania among them -- and the District of Columbia. Romney would lay claim to 206, from probable victories in 23 states that are strong Republican turf or tilt toward the Republicans, including North Carolina.

Up for grabs are 83 electoral votes spread across Colorado, Florida, Ohio, New Hampshire, Virginia and Wisconsin. Of those, Republicans and Democrats alike say Obama seems in slightly better shape than Romney in Ohio and Wisconsin, while Romney appears to be performing slightly better than Obama or has pulled even in Florida and Virginia.

Romney, who described himself as "severely conservative" during the Republican primary campaign, has shifted sharply in recent weeks to appeal to the political centre and highlights what he says was his bipartisan record as governor of Democratic-leaning Massachusetts.

Making his closing case to voters at his first stop Sunday in Des Moines, Iowa, Romney pledged, if elected, to work with Democrats to restore the American dream and bring the economy roaring back to life.

"We're Americans. We can do anything," Romney said. "The only thing that stands between us and some of the best years we can imagine is a lack of leadership -- and that's why we have elections."

After his stops Sunday in Iowa and Ohio, Romney moves on to Pennsylvania and Virginia .

In the final days of his final campaign, Obama has been imploring crowds at his rallies -- and the wider electorate -- to let him finish what he started. The nation has been bruised by recession and war, he contends, but remains resilient and is coming back.

Obama, too, said he is willing to work across party lines to break Washington's gridlock, but assured some 14,000 supporters who gathered to hear him and former President Bill Clinton in Concord, New Hampshire, that he would not compromise key Democratic priorities such as health care and college financial aid.

"I know I look a little bit older, but I've got a lot of fight left in me," Obama said. "We have come too far to turn back now. We have come too far to let our hearts grow faint. It's time to keep pushing forward."

Obama had a full schedule Sunday, with campaign stops that also take him to Florida, Ohio and Colorado.

The economy has been the dominant issue of the campaign despite detours into foreign policy and social issues. At week's end, the final jobs report before Tuesday's election gave one last economic snapshot, showing the U.S. adding a solid 171,000 jobs and more than a half-million Americans joining the workforce. But the jobless rate of 7.9 per cent was still higher than when Obama took office.

More than 27 million Americans have already voted in 34 states and Washington, D.C. Obama holds an apparent lead over Romney in several key states such as Iowa and Nevada. 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 voting.