BEDFORD HEIGHTS, Ohio—For Mitt Romney's campaign, the location was nothing more than a friendly business that had agreed to host a rally to promote the candidate's policies toward small businesses and manufacturing.

But it was hard not to view Romney's midday appearance at American Spring Wire, a company that makes wire that bounces back into place, as a possible metaphor for the candidate's electoral hopes in this crucial swing state.

"It goes right back to where it started," Romney told a crowd of several hundred people here, explaining how spring wire works.

He's hoping the same can be said of his race in this state. The Republican candidate's impromptu tutorial came as a series of new polls found that after months of a close race here between President Barack Obama and Romney, the GOP's chances in Ohio appear to be slipping away.

A New York Times/CBS News/Quinnipiac poll released on Wednesday found Obama leading Romney among likely Ohio voters by 10 points, 53 percent to 43 percent. It came on the heels of a Washington Post poll released on Tuesday that found Obama besting Romney by 8 points in the state.

They were the third and fourth polls in a row to find Obama expanding his lead in the Buckeye State—a move that prompted ABC News to change its projection of Ohio being a "toss up" state in November to one that "leans Obama."

As Romney spoke, Obama was campaigning on the other side of the state, holding his own rally at Bowling Green State University. There, the president lit into his Republican opponent, accusing Romney of wanting to gut education by giving wealthy Americans a tax cut. He also seized upon Romney's suggestion captured in a secretly filmed video at a fundraiser that 47 percent of Americans view themselves as "victims" and are too dependent on the government.

"I don't believe we can get very far with leaders who write off half the nation as victims," Obama said.

The dueling visits by Obama and Romney offered a hint at what has been one of the GOP candidate's major problems in Ohio: He's been largely outmaneuvered by his Democratic opponent, who has lavished money and attention on Ohio since he took office.

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Wednesday marked Obama's 13th visit to the state so far this year—and his 29th since taking office, according to his campaign. That does not include an appearance Obama made in the state just days before he was officially inaugurated in January 2009—a visit many at the time said was the unofficial kickoff to his 2012 campaign.

Obama has significantly outspent Romney when it comes to television advertising in the state: Obama dropped $41 million since May compared with just $21 million by Romney, says National Journal. Outside Republican groups have made up some of that ground—chipping in about $20 million in ads in the state, according to National Journal—but the Obama campaign has spent tens of millions more building up its staff and ground operation in Ohio. And the effort appears to be having an impact on the polls, especially on the issue of the economy.

In Ohio, a state that has been hard-hit by the loss of manufacturing jobs, the Romney team believed it would benefit from voter angst over the economy. But while the NYT/CBS/Quinnipiac poll found the economy is still the top issue for Ohio voters, Obama now holds a 6-point advantage over Romney when it comes to who voters believe would do a "better job." When presented with the same question in polls during July and August, the candidates were tied.

Romney still has an advantage on the economy among Ohio independents: According to the NYT/CBS/Quinnipiac poll, 51 percent of independent voters think he would best handle the economy, compared with 45 percent for Obama.

But Romney is being hurt by his drop in support among women voters, who overwhelmingly prefer Obama on the issue of the economy—59 percent to Romney's 37 percent. Overall, female voters in Ohio prefer Obama in the race, 60 percent to Romney's 35 percent.

The Romney team has worked to make up its deficit among female voters in Ohio and other battlegrounds, appealing to them through television ads on issues like the growing federal deficit—one of the few areas where Romney continues to have an advantage over Obama.

Nevertheless, Romney aides have refuted any suggestions the candidate is in real trouble in this state. The Romney campaign has downplayed public polls, insisting its internal numbers show the race much closer—though it declined to offer specifics.

Speaking to reporters on Tuesday, Rich Beeson, Romney's political director, said the race in Ohio is still "inside the margin of error" and accused the Obama campaign of "spiking the ball at the 30-yard line." But he declined to say whether there is a path to victory for Romney if he can't win Ohio.

"The public polls are what the public polls are," Beeson said. "I kind of hope the Obama campaign is basing their campaign on what the public polls say. We don't. We have confidence in our data and our metrics."

In response, Obama campaign spokeswoman Jen Psaki trotted out her own sports metaphor, so to speak, likening the campaign to a horse race.

"We don't get too whipped up when we're up, or too whipped up when we're down. And we're running this race in every single swing state like we're five points down. If we need to pass out horse blinders to all of our staff, we will do that," Psaki told reporters traveling with the president.

But, she added, "As time progresses, the field is looking like it's narrowing for them. And so, in that sense, we'd rather be us than them, because we want a field—or a path, I should say—where you can drive a Mack truck through it, not one where you can drive a little scooter through it."