One final jobs report before Election Day and the big storm threatening the East Coast loom large as President Barack Obama and Republican Mitt Romney head into the final full week of campaigning in a race that polls show is extraordinarily close.

Democrats claim math is on the President’s side. Republicans insist Mr. Romney’s got the momentum.

Mr. Obama is banking on his get-out-the-vote efforts in the most competitive states. He’s also making personal appeals as he encourages Americans to stick with him for a second term.

In pursuit of the 270 electoral votes needed for victory, each candidate is starting to make his closing arguments. The goal is to win over the narrow slice of undecided, independent voters, moderates and women in particular, and to persuade supporters to vote on November 6, if not earlier in the many states where voting is already under way. Roughly one-third of the electorate will have voted before Election Day.

Presidents are not elected by national popular vote, but in state-by-state contests that allocate electoral votes. Each state gets one electoral vote for each of its representatives in the House and Senate. The winner needs a majority of the 538 electoral votes.

Mr. Obama is ahead in states and the District of Columbia representing 237 electoral votes; Mr. Romney has a comfortable lead in states with 191 electoral votes. There are nine contested battleground states which are not reliably Democratic or Republican that are too close to call.

The question now is whether the momentum Mr. Romney picked up after the first presidential debate on October 3 is growing and can overcome the President’s strong voter-identification and early voting efforts in the most competitive states.

The campaigns are scrambling to tweak schedules, shift manpower and pump millions of more dollars into TV ads in battleground states that will determine the outcome. Deep-pocketed outside groups are paying for direct mail, automated phone calls and other get-out-the-vote efforts.

Total campaign spending has exceeded $2 billion, making this presidential race the most expensive in the history of electoral politics.

Any number of factors still could shift the race.

A massive weather system bearing down on the East Coast threatens to complicate the final days of campaigning and early voting across at least four pivotal states ew Hampshire, North Carolina, Ohio and Virginia.

Mr. Romney scrapped plans to campaign in Virginia on Sunday, and switched his schedule for the day to Ohio.

En route to a campaign rally on Saturday in New Hampshire, Mr. Obama held an airborne conference call with administration officials about the federal government’s role in minimizing storm damage and ensuring a speedy recovery effort.

Vice President Joe Biden cancelled a Saturday rally in coastal Virginia Beach, Virginia, to allow local officials there to focus on disaster preparedness and local security concerns. But he went ahead with an appearance in Lynchburg, which is inland.

Mr. Biden said Mr. Romney and Mr. Ryan are fleeing from their record to appear more moderate than they are. They “are counting on the American people to have an overwhelming case of amnesia,” he said.

Mr. Romney, who has been striking a more moderate tone as he courts women and independents in the campaign’s home stretch, campaigned across Florida on Saturday with a pledge to “build bridges” with the other party.

But he coupled that message with digs at Mr. Obama for “shrinking from the magnitude of the times” and advancing an agenda that lacks vision.

Mr. Romney held three events across Florida on Saturday, timed to coincide with the first day of in-person early voting in a state that went for Mr. Obama four years ago and where 29 electoral votes are up for grabs this time.

Mr. Obama hauled his campaign to New Hampshire, where he accused Mr. Romney of making life more expensive for the middle class during his term as Massachusetts governor.

“All he’s offering is a big rerun of the same policies,” Mr. Obama told a crowd of 8,500 gathered at an outdoor rally in Nashua on an unseasonably warm October day.

The President said Mr. Romney even raised fees in Massachusetts on obtaining a birth certificate, “which would have been expensive for me.” It was a veiled reference to opponents of the president who have incorrectly said he was born outside the United States.

Mr. Romney’s running mate, Rep. Paul Ryan, worked his way across rainy, chilly Ohio, on a two-day bus trip. At a factory in New Philadelphia in eastern Ohio, Mr. Ryan told a crowd of 1,000 supporters that Mr. Obama has not made the case that he deserves another four years in the White House.

With each candidate claiming to be best able to revive the struggling economy, the latest jobs report due Friday from the Labor Department will shine an 11 hour spotlight on the country’s health four days before most people vote. Last week, the most recent snapshot of economic growth showed the U.S. recovery remains tepid.

At Mr. Romney’s Boston base and Mr. Obama’s Chicago headquarters, aides are focused on the factors they can control. That means how and where their candidate spends his time and money in the nine battleground states Colorado, Florida, Iowa, New Hampshire, Nevada, North Carolina, Ohio, Wisconsin and Virginia.

Both sides acknowledge that Mr. Obama has a larger campaign organization on the ground in most states, and that Democrats have an edge in the push to get supporters to the polls early in many of the most competitive states.

Obama advisers insist the President is leading or tied in all nine of those states, though strategists in both parties say North Carolina has shifted toward Mr. Romney in recent days. Romney aides insist that state-based polling underestimates the former Massachusetts governor’s popularity with independents.

Obama aides say they expect the demographics of the electorate to look similar to the 2008 election, with slight increases in black and Hispanic voters.

While Mr. Romney and Mr. Obama are deadlocked in national polls, there were signs that the burst of momentum Mr. Romney got from the debates had waned in Ohio, Virginia and elsewhere. Because Mr. Obama starts with more states and votes solidly in his expected win column, Mr. Romney’s team has fewer ways to reach the 270 electoral votes.

Both sides agree this race will be won at the margins.

That explains why Mr. Obama’s campaign has been working hard to undercut Mr. Romney’s support among women by citing links between Mr. Romney and an Indiana Senate candidate, Richard Mourdock, who drew fire for saying that pregnancies resulting from rape are “something God intended.” Romney aides said he disagreed with the comment but Mr. Romney himself refused to call on Mr. Mourdock to remove TV ads the Republican presidential nominee had filmed for him.

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