WESTERVILLE, Ohio — Slipping in states that could sink his presidential bid, Republican Mitt Romney declared Wednesday that “I care about the people of America” and can do more than President Obama to improve their lives. In an all-day Ohio duel, Obama scoffed that a challenger who calls half the nation “victims” was unlikely to be of much help.

Romney’s approach reflected what he is up against: a widening Obama lead in polls in key states such as Ohio, the backlash from a leaked video in which he disparages Obama supporters as government-dependent people who see themselves as victims, and a campaign imperative to make his policy plans more plain.

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Republican presidential candidate, former Massachusetts Gov. Mitt Romney speaks during a campaign stop at American Spring Wire, Wednesday, Sept. 26, 2012, in Bedford Heights, Ohio. (AP Photo/ David Richard)

New opinion polls, conducted after the video became public, show Obama opening up apparent leads over Romney in battleground states, including Ohio and Virginia. And majorities of voters in Florida, Ohio and Pennsylvania say Romney’s policies would favor the rich over the middle class or the poor.

Specifically in Ohio, two surveys show the president crossing the 50 percent mark among likely voters. A Washington Post poll found Obama ahead 52 percent to 44 percent among those most likely to turn out, and a Quinnipiac University/CBS News/New York Times poll showed a 10-point Obama lead among definite voters.

With under six weeks to go, and just one week before the first big debate, Obama’s campaign reveled in the latest public polling — but tried to crush any sense of overconfidence. “If we need to pass out horse blinders to all of our staff, we will do that,” said campaign spokeswoman Jen Psaki.

The day’s setting was Ohio, where Obama’s momentum has seemed to be growing. No Republican has ever won the White House without carrying Ohio.

Romney, eager to project confidence and brush aside suggestions that he was faltering, went after working-class voters outside Columbus and Cleveland before rolling to Toledo. Obama rallied college crowds at Bowling Green State University and Kent State University, reminding Ohioans that their state allows them to start casting ballots next week. Early voting has already begun in more than two dozen other states.

For Romney, in his appearances and in a new TV ad in which he appeals straight to the camera, it was time for plain talk to contrast himself with Obama.

“There are so many people in our country who are hurting right now. I want to help them. I know what it takes,” Romney told the crowd in Westerville. “I care about the people of America, and the difference between me and Barack Obama is I know what to do.”

Asked in an interview about his ability to empathize with ordinary Americans, Romney cited the health care law he championed while governor of Massachusetts. It’s a topic Romney usually doesn’t raise because Obama cites the initiative as the basis for his own health care overhaul. Conservatives despise what they call “Obamacare” — Romney has vowed to repeal and replace it if elected — and tend to oppose the idea of universal health coverage.

“Don’t forget — I got everybody in my state insured,” Romney told NBC News while in Toledo. “One hundred percent of the kids in our state had health insurance. I don’t think there’s anything that shows more empathy and care about the people of this country than that kind of record.”

That message so late in the campaign — a presidential nominee declaring his concern for all the people of the country — was part of his widening effort to rebound from his caught-on-video comments at a fundraiser.

In those comments, made last May but only recently revealed, Romney said “47 percent of the people” pay no federal income tax, will vote for Obama no matter what, see themselves as victims, think the government must care for them and do not “take personal responsibility and care for their lives.”

Noting anew the Romney video comments, Obama said Wednesday: “We understand that America is not about what can be done for us. It’s about what can be done by us together, as one nation, as one people.”

And he added: “You can’t make it happen if you write off half the nation before you take office.”

Romney was showing signs of picking up his pace, and he did not mince words about his expectations.

“Were we to re-elect President Obama there is no question in my mind we’d face four more difficult years,” he said. “If, instead I — no, instead, when I become president, we’re going to get this economy growing again, we’re going to do the things that ignite this economy.”

Romney scheduled a blizzard of interviews with ABC, CBS and NBC, his second round of broadcast network appearances in three days after weeks of ignoring their requests. He also did interviews Tuesday with Fox News and CNN.

“I’m very pleased with some polls, less so with other polls,” he told ABC. “But frankly, at this early stage, polls go up, polls go down.”

The new Romney TV ad, at 60 seconds, is a longer and softer approach in which he speaks about people struggling to pay for food and gas with falling incomes.

At a factory in Bedford Heights, Romney appeared Wednesday on a stage surrounded by visual evidence of Ohio’s manufacturing base — giant coils of steel wire, metal beams, yellow “caution” signs — and spoke as machines whirred in the background. He appeared with Mike Rowe, an everyman TV personality and pitchman.

The campaigns tried, too, for footholds on other fronts.

Both sides kept up their attempts to paint each other as weak in dealing with China, efforts aimed at wooing support from working-class voters whose jobs might suffer from imports from China.

Romney also focused Wednesday on interest paid on the national debt, a subject he hasn’t regularly discussed in his standard campaign speech. His comments came after a Washington Post poll showed the federal debt and deficit are the one set of issues where he has an advantage over Obama with likely voters.

Romney’s running mate, Paul Ryan, took a sharper approach. He told radio host Sean Hannity that Obama was using hollow tactics to paint his opponents as evil.

“He’s basically trying to say, ‘If you want any security in your life, stick with me. If you go with these Republicans they’re going to feed you to the wolves. It’s going to be a dog-eat-dog society,'” Ryan said.

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