WESTERVILLE, Ohio (Reuters) - Republican presidential candidate Mitt Romney expressed empathy for unemployed Americans on Wednesday in what appeared to be an effort to repair the damage from comments he made in a leaked videotape that has sent his poll numbers on a downward slide.

Republican presidential candidate and former Massachusetts Governor Mitt Romney speaks at a campaign rally in Westerville, Ohio September 26, 2012. REUTERS/Brian Snyder

“I’ve been across the country. My heart aches for the people I’ve seen,” Romney told an enthusiastic crowd in Westerville on the second day of a bus tour across a state considered a must-win for him in the November 6 election.

On a day the candidate was joined by golf legend and Ohio native Jack Nicklaus, a new poll by Quinnipiac University and The New York Times spelled trouble for Romney.

It said that Democratic President Barack Obama - who also campaigned in Ohio on Wednesday - leads Romney in Ohio by 10 percentage points and is ahead in two other important states - Florida and Pennsylvania - by similar margins.

Ohio and Florida are politically divided states central to Romney’s hopes to amass the 270 electoral votes needed for victory, and losing either could be disastrous for the Republican.

The survey suggested that Romney, who was trailing Obama by a smaller margin at the beginning of last week, has been significantly damaged by the disclosure of a secretly taped video of him speaking at a private fundraiser in May.

In the video, Romney - a former private equity executive with a fortune estimated at up to $250 million - tells wealthy donors to his campaign that 47 percent of Americans are “victims” who depend on government, don’t pay federal income taxes and are unlikely to support him.

The airing of the comments last week sent Romney’s campaign into crisis mode. Democrats were quick to point out that the “47 percent” to whom Romney referred - those who receive some form of government benefits - includes not just the poor but also working-class families, members of the military and the elderly, some of whom Romney has depended upon for support.

“The furor over his 47 percent remark almost certainly is a major factor in the roughly double-digit leads President Barack Obama has in Florida, Ohio and Pennsylvania,” said Peter A. Brown, assistant director of the Quinnipiac University Polling Institute.

The Reuters/Ipsos daily tracking poll on Wednesday had Obama essentially maintaining the lead he built over Romney last week among likely voters nationwide, 49 percent to 43 percent.

‘SO MANY PEOPLE ... HURTING’

Romney often talks about the people he meets while campaigning, but he usually does so to illustrate a story about a successful business - a man who made sandwiches in his garage and grew his company into a national chain, a woman who makes furniture for hospital waiting rooms.

On Wednesday, Romney took a different tack, and told stories of economic hardship that he linked to Obama’s stewardship of a sluggish economy.

Ohio is a relatively challenging place for Romney’s economic message. The state unemployment rate is 7.2 percent, below the national rate of 8.1 percent.

One in eight jobs in Ohio is linked to the automobile industry, and Obama’s campaign has been reminding Ohio residents that he pushed through the industry bailout, and Romney opposed it.

“I was yesterday with a woman who was emotional and she said, ‘Look, I’ve been out of work since May.’ She was in her 50s. She said, ‘I don’t see any prospects. Can you help me?’ ” Romney said.

“There are so many people in our country that are hurting right now,” Romney added. “I want to help them. I know what it takes to get an economy going again and creating jobs.”

The Romney campaign amplified this message with a new television ad featuring the candidate speaking directly into the camera.

“President Obama and I both care about poor and middle-class families,” Romney says in the ad. “The difference is, my policies will make things better for them. We shouldn’t measure compassion by how many people are on welfare.”

In his Westerville speech, Romney fought back against claims by Obama’s campaign that Romney’s proposed across-the-board 20 percent tax cut would mostly benefit the wealthy. Romney also said he would limit some tax deductions.

“By the way, don’t be expecting a huge cut in taxes because I’m also going to be closing loopholes on deductions,” he said.

Nicklaus added some star power to Romney’s appearance. The golf great likened the election of Obama in 2008 to an errant shot. Golfers can’t fret over a bad shot but must move on, he said.

“America cannot afford four more years of Barack Obama’s failed policies,” Nicklaus said. “We need a real recovery.”

Romney campaigned in Ohio with Paul Ryan, his vice presidential running mate, on Tuesday. It was their first appearance together in more than three weeks, as aides promised a more aggressive phase of campaigning after Romney spent much of the past two weeks raising money and holding few public rallies.

Ryan campaigned on Wednesday in Colorado, another battleground state where polls show Romney in a tight race with Obama.