NASHUA — With just 10 days until the election, President Barack Obama made his sixth 2012 campaign visit to the Granite State on Saturday, underscoring New Hampshire's traditional significance in the race for the White House in a speech to a crowd of thousands.

Republican candidate Mitt Romney, who campaigned in Florida on Saturday, a state with 29 electoral votes, is scheduled to visit New Hampshire on Tuesday.

Obama spoke in front of Elm Street Middle School on Saturday afternoon, touting his presidential achievements and rebutting the claims of his opponent.

“These four electoral votes right here could make the difference,” Obama told the 8,500 spectators.

Although the state offers just four electoral votes toward the 270 necessary to win the election, certain circumstances could prove New Hampshire decisive. When Al Gore lost the 2000 election to George W. Bush, New Hampshire was one of the deciding factors that led to Bush's victory. Had Gore won New Hampshire, he would have won the race.

Hurricane Sandy forced Romney to shuffle his final-days campaign schedule, canceling three planned Virginia events and shifting his time to Ohio instead after a flyaround in Florida, where early voting kicked off Saturday.

Romney, who did not discuss the pending storm during his first stop at a rally in Pensacola, told the packed crowd at an airport hangar in Kissimmee for his second event that he had spoken to Republican Virginia Gov. Bob McDonnell, who had said the first responders there need to keep their eyes on storm readiness.

“I hope you'll keep ... the folks in Virginia and New Jersey and New York and all along the coast in your minds and in your hearts,” Romney told the crowd, to applause. “You know how tough these hurricanes can be and our hearts go out to them.”

Romney and his surrogates — including Sen. Marco Rubio, who has strong backing in Florida generally and with Hispanic voters — described the election to supporters as a “change” race, and suggested Obama's team is running an ideas-vacant race that's all about attacking.

“He has so many attacks on me — it's like, you know, there are other ways to go after me,” Romney said in Kissimmee. “Just go after me with the truth. You don't need to make up things. But he makes things up he knows aren't true and frankly I think that's in part why his campaign isn't making much progress because people recognize that this is a critical time.”

But while Romney blasted President Obama's policies and the way he's run his campaign, he focused on working with Democrats, in a contrast to the scorched-earth criticisms of Rubio and Rep. Jeff Miller before the Republican nominee took the stage.

“Paul Ryan and I are going to have to do what we've done before. Which is reach across the aisle,” Romney said. “We have to build bridges to people in the other party. We have to recognize this is not a time in America for us to pull back, and to divide and to demonize. It's a time in America for us to come together, to look for common ground, for places where we have agreement.”

He argued that Ryan, whose Medicare plan has been the focus of a deluge of Democratic ads and mailers, had done that when he worked on that very plan.

Earlier, he said the President's “agenda keeps getting smaller and smaller and smaller, not just for our military but for Medicare, for jobs. This is not a President who has been able to stand up to the challenge of the times.”

In Nashua, the President said the election offers a choice between two fundamentally different visions for America. “We believe in the values that build the largest middle class, the strongest economy the world has ever known. The promise that hard work will pay off.”

He said a nation's prosperity isn't measured by how many millionaires and billionaires are produced, but how well the typical family is doing.

Obama also raised issues of significance to women several times, painting his opponent as attempting to take their rights away. “We know we're better off when politicians in Washington aren't allowed to make decisions about health care that women are perfectly capable of making for themselves,” he said.

Obama said Romney is offering a rerun of the same policies that led to the suffering of the economic decline.

Obama, citing his stimulus plan, vowed to hire 100,000 math and science teachers, train 2 million workers and work with universities to keep tuition down.

“If you're willing to work with me ... I'm going to win Hillsborough County, we'll win New Hampshire again,” Obama said. “We'll finish what we started, and we'll remind the world why the United States of America is the greatest nation on earth.”

Miller, for his part, made a reference to the Benghazi violence, a line of attack on Obama that Romney has basically dropped himself.

“America deserves a President that does not divide but unites this country. America deserves a President who understands its military and its weapons,” he said, mentioning the four slain diplomats before the crowd drowned him out with chants of “USA! USA!”

“Mr. President, the phone rang and you didn't answer it,” he said.

Material from Politico.com was used in this story.