WESTERVILLE, Ohio—Mitt Romney kicked off a day of campaigning in this battleground state by insisting his "heart aches" for struggling Americans and that he is better prepared than President Barack Obama to help those who are "hurting" under the tough economy.

Speaking at a rally located in a swing district just outside Columbus, Romney kept repeating his empathy for people out of work and trying to pay their bills—insisting that he will do his "very best to help" those in need "when I am president."

"I've been across this country, and my heart aches for the people I've seen," Romney told a crowd of several hundred people here. "There are so many in our country that are hurting right now. I want to help them."

Relating the story of an unemployed woman he met at a rally on Tuesday, Romney insisted over and over that he has "what it takes to get the economy going again."

"I care about the people in America," he said. "And the difference between me and President Obama is I know what to do, and I will do what it takes to get this economy going."

Romney's remarks came as yet another public poll found him losing significant ground to Obama in Ohio, which has been considered a must-win state for his campaign. A New York Times/CBS News/Quinnipiac poll released Wednesday found Obama leading Romney by 10 points, 53 percent to 43 percent. It came on the heels of a Washington Post poll released Tuesday that found Obama leading Romney by 8 points in Ohio.

Top Romney aides have downplayed the public polling—suggesting their internal numbers remain close. But Romney's message on the stump Wednesday seemed to be informed by findings in the latest round of surveys, including stats from the NYT/CBS/Quinnipiac poll showing that he still holds an advantage over Obama when it comes to who would be best equipped to handle the growing federal deficit.

Campaigning in a high school gym here, Romney spoke against the backdrop of a constantly updating national debt clock—a prop that hasn't been used at his rallies for a while. He spoke at length about why the growing deficit is a major crisis for the country—one, he claimed, that Obama is ignoring.

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Highlighting the nation's $16 trillion in debt, Romney said of Obama, "If he were re-elected, I can assure you, it would be almost $20 trillion debt."

Looking to offer context, Romney added, "What is a trillion? It's a thousand billions."

Romney also called for efforts to "reform our tax system"—but at the same time, he seemed to downplay the idea of instituting major tax relief should he be elected president.

"Small businesses most typically pay taxes at the individual tax rate. And so our individual income taxes are the ones I want to reform. Make them simpler. I want to bring the rates down," Romney said.

But, he added, "Don't be expecting a huge cut in taxes because I'm also going to lower deductions and exemptions. But by bringing rates down we will be able to let small businesses keep more of their money so they can hire more people."

Amid criticism from members of his own party that he hasn't had any "fire in the belly" on the trail, Romney seemed more passionate on the stump than he's been in weeks.

Ahead of his arrival onstage, aides played for the crowd a powerful biographical video of Romney that first aired during the Republican National Convention. The video featured interviews with Romney's wife, Ann, and their five sons. Those in the gym seemed captivated by the clip. The video has been the subject of questions among Republicans lately about why the Romney campaign isn't doing more to broadcast it throughout swing states, where polls show voters are still skeptical about Romney personally.

Romney's move to emphasize his compassion with voters here came as his campaign continues to do damage control over the candidate's suggestion in a secretly taped video at a May fundraiser that Obama supporters—which he calculated to be "47 percent" of the country—see themselves as victims and are too dependent on the government.

Ahead of his rally, the Romney campaign released an ad featuring the candidate speaking directly to the camera about "compassion" and his desire to help the middle class.

Joining Romney onstage was golf legend Jack Nicklaus, who is from the area. He offered up a full-throated endorsement of the GOP candidate, arguing that people "want us to be like America to be like we were."

Romney would "ignite a real recovery" if elected, Nicklaus said.