PENSACOLA, Fla. — 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 polls show is extraordinarily close.

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

“We’re seeing more and more enthusiasm, and more and more support,” a confident Romney says in messages to supporters, arguing that his performances in the three presidential debates has reinvigorated his campaign and created a national movement.

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. During a whirlwind tour last week through some of the most pivotal states, he said, “After all these years, you know me. You know I mean what I say.”

In pursuit of the 270 electoral votes for victory, each nominee 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 Nov. 6, if not earlier in the many states where voting is under way. Roughly one-third of the electorate will have voted before Election Day.

The question now is whether the momentum Romney picked up after the debates is growing and can overcome the president’s strong voter-identification and early voting efforts in the tightest states.

The campaigns are scrambling to tweak schedules, shift manpower and pump millions of more dollars into TV ads in the nine 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.

But there’s a risk that all those commercials, phone calls and mailings have caused many people to tune out.

“I’m so sick of those commercials,” said Cora Blakey, a retiree who stood in long lines with about 13,000 people to see Obama last week at an outdoor park in Las Vegas. “Everybody’s bashing everybody. When they come on, I turn the channel.”

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 —New Hampshire, North Carolina, Ohio and Virginia.

With each man claiming to be best able to revive the struggling economy, the latest jobs report due Friday from the Labor Department will shine an 11th-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 Romney’s Boston base and 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 states that will decide the outcome — Colorado, Florida, Iowa, New Hampshire, Nevada, North Carolina, Ohio, Wisconsin and Virginia.

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

Obama’s campaign is confident about Ohio, Iowa, Nevada and Wisconsin; the race looks tighter in Colorado, Virginia and Florida. Democrats also voiced confidence in New Hampshire, though there is little early voting in the state, making it harder to gauge now.

Despite the heavy focus on turnout, Obama’s campaign says it is still working to persuade undecided voters and soft Romney supporters to back the president. That’s why Obama is focusing much of his travel in the campaign’s final stretch on swing areas of competitive states, including Green Bay, Wis., Orlando and Denver. Romney is focused on Ohio, Florida and Wisconsin and expects to travel to New Hampshire on Tuesday.

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. They attribute that both to natural population growth and the campaign’s efforts to boost minority voter registration.

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

Seeking to create more options and influence voters in neighboring states, Romney has made modest television advertising investments in Minnesota and Maine, competing in states that haven’t supported a Republican in at least two decades.

Ohio and Wisconsin, where Democrats have an edge, have emerged as linchpins to his strategy.

Democratic strategists say that Romney’s opposition to the auto bailout that resurrected the American auto industry continues to hurt him across the industrial Midwest. Obama seized on Romney’s position during last week’s third and final debate, a moment Democrats say helped reverse the Republican candidate’s momentum among working class white voters, an important constituency in blue-collar Ohio.

“To his credit, Romney got himself back into the race. But it’s not enough,” said Tad Devine, a Democratic strategist and senior adviser to 2000 and 2004 presidential nominees Al Gore and John Kerry.

Still, Romney was greeted by large enthusiastic crowds in the thousands in Ohio, Iowa and Florida in recent days, a sign Republican pollsters and strategists attributed to higher intensity of support from his campaign’s base.

Romney aides suggest that swing-state polls overestimate Obama’s support. Obama aides dismiss polls showing Obama losing support among women.

“It’s going to be a tight race right to the end,” said Romney senior strategist Eric Fehrnstrom. “But we’re riding a wave and it hasn’t hit the beach yet.”

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

That explains why Obama’s campaign has been working hard to undercut Romney’s support among women by citing links between 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 Romney himself refused to condemn the remark or call on Mourdock to remove TV ads the GOP presidential nominee had filmed for him.

The renewed attention on abortion came just as polls showed Romney having narrowed Obama’s advantage with women. Now Democratic pollsters say they see evidence that Romney may be losing those gains among women, especially in Virginia and Colorado.

Not that he’s ceding ground.

“These are tough times for middle-income Americans,” Romney said Friday night in North Canton, Ohio. “How many single moms these days are scrimping and saving so they can put a good meal on the table at the end of the day for their kids?”