WESTERVILLE, Ohio — Slipping in states that could sink his presidential bid, Republican Mitt Romney declared Wednesday that he cares 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 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 those 47 percent of Americans who pay no federal income taxes as government-dependent victims, and a campaign imperative to make his policy plans more plain.
With under six weeks to go, and just one week before the first 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. It is also a state no Republican has won the White House without carrying. Romney went after working-class voters outside Columbus and Cleveland before rolling to Toledo. Obama rallied college crowds at Bowling Green and Kent State, reminding Ohioans their state allows them to start casting ballots next week.
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,’’ Romney told the crowd in Westerville. “I want to help them. I know what it takes. I care about the people of America, and the difference between me and Barack Obama is I know what to do.’’
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 fund-raiser.
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, are victims, think the government must care for them, and do not take personal responsibility and care for their lives.
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.
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.
He 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.
At one point Wednesday, the two candidates spoke from different sections of northern Ohio at the same time, their scenery as different as their message.
At a factory in Bedford Heights, Romney appeared 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.
Obama appeared at two packed college basketball arenas, delivering his message first to a boisterous crowd of more than 5,000 at Bowling Green State University and then to 6,000 screaming supporters at Kent State University.
He said a student who introduced him broke his wrist during a game of ultimate Frisbee. Exhorting the crowd to vote, he said, ‘‘You’ve got to play through injuries.’’