Mitt Romney, rallying Republicans in the state's aptly named town of Defiance, mocked Obama's "incredibly shrinking" campaign and stole the president's 2008 mantra, promising "big change" if he wins on November 6.
The latest sharp exchanges came as polls showed the White House up for grabs, with Romney ahead by a nose nationally, but Obama standing firm in the key swing states that could hand him a second four-year term.
The president on Thursday won the endorsement of Colin Powell -- an African-American Republican who served in both Bush presidencies -- sparking controversial remarks by a Romney surrogate who suggested race was a factor.
"When you have somebody of your own race that you're proud of being president of the United States, I applaud Colin for standing with him," top Romney advisor John Sununu said about Powell, who also backed Obama in 2008.
Sununu later issued a statement backtracking on the remarks, saying: "I respect the endorsement decision (Powell) made, and I do not doubt that it was based on anything but his support of the president's policies."
The remarks by Sununu, who is known for fiery media appearances, could inject race into a campaign Romney has tried to keep focused on the economy.
Earlier on Thursday, Obama lambasted Romney for opposing his bailout of the auto industry as he campaigned in Ohio, a perennial battleground in which car manufacturing supports one in eight jobs.
"I refused to walk away from those workers, I refused to walk away from those jobs. I bet on American workers. I would do it again because that bet always pays off," Obama roared, in a populist pitch for blue collar votes.
Obama ended an eight state tour of more than 7,000 miles with 11 days to go before he asks Americans to defy the omens of a weak economy and high unemployment by voting to renew his lease on the White House.
The president's aides are privately signaling increasing confidence that he will prevail. But Romney has sought to convince his supporters that he has the momentum in the final stretch.
"We want big change," Romney told a 12,000-strong crowd in Defiance, accusing Obama of waging a nasty campaign drained of new ideas.
"This is a time for big challenges, and a time of big opportunities, we have a big choice. And frankly we're going to elect a president that's willing to make big changes, and I will," Romney, a former Massachusetts governor, said.
Romney blames Obama for four years of lackluster US growth, while the Democratic incumbent warns that Americans have come too far out of recession to risk reversing the progress under Republicans.
Earlier, Obama became the first sitting president to cast an early vote, in a successful grab for news coverage also designed to mobilize his supporters to register their ballots early.
Hours later, in a striking example of the theatrical power possessed by an incumbent president running for re-election, Obama landed before 12,000 people who had waited for hours at a lakefront airport in Cleveland.
The converted Boeing 757 serving as Air Force One, the codename given to any aircraft carrying the president, pirouetted on its nose wheel in front of the cheering crowd before Obama bounded down the steps and onto a stage.
The closer the election gets, the more the bad feeling between Romney and Obama seems to show.
In a Rolling Stone interview published Thursday, Obama told the magazine's executive editor Eric Bates, that children had excellent political instincts and could spot a "bullshitter."
The comment was widely viewed as a jab at Romney, who Obama has accused of lacking principle and shifting positions for political gain. The remark prompted an acidic response from Romney spokesman Kevin Madden.
"President Obama is rattled and on the defensive. He's running on empty and has nothing left but attacks and insults. It's unfortunate he has to close the final days of the campaign this way," he said.
Obama's team says he still has multiple routes to the 270 electoral votes needed to win the White House.
In two days, he toured battlegrounds Iowa, Colorado, Nevada, Florida, Virginia and Ohio, stopped in California to appear on a late night talk show and made it home to Chicago.
Romney has also done his share of map hopping, but on Thursday he focused squarely on Ohio, where the latest average of polls by the RealClearPolitics website had Obama up by two points.
NBC/Wall Street Journal polls Thursday showed Obama up three points on Romney in Nevada, where he also leads early voting, and tied with Romney in the Rocky Mountain battleground of Colorado.
Romney, however, was up three points in an ABC News/Washington Post poll of likely voters.
Sununu's race comment threatened to ignite another controversy as Romney was still struggling to contain fallout from comments about rape and abortion by Indiana Senate candidate Richard Mourdock, whom he has endorsed.
Mourdock had said pregnancy caused by rape was "something God intended to happen" offering an opening for the Obama campaign, which accuses Romney of backing a return to 1950s-era social policies.
Romney's team says their candidate does not agree with Mourdock's views but still supports him in the Senate race.