Charges of negative campaign tactics were high on the program, too.
"Senator Obama has consistently said I would force people to have health care whether they can afford it or not," said Clinton, insisting it was not true.
Responding quickly, Obama countered that former first lady had consistently claimed his plan "would leave 15 million people out ... I dispute that. I think it is inaccurate," he said.
The tone was polite yet pointed, increasingly so as the 90-minute session wore on, a reflection of the stakes in a race in which Obama has won 11 straight primaries and caucuses and Clinton is in desperate need of a comeback.
Clinton also said as far as she knew her campaign had nothing to do with circulating a photograph of Obama wearing a white turban and a wraparound white robe presented to him by elders in Wajir, in northeastern Kenya.
The gossip and news Web site The Drudge Report posted the photograph Monday and said, without substantiation, that it was being circulated by "Clinton staffers."
"We have no evidence where it came from," Clinton said, making clear that's not the kind of behavior she wants in her campaign. "I take Senator Clinton at her word that she knew nothing about the photo," Obama said.
The two rivals, the only survivors of a grueling primary season, sat about a foot apart at a table on stage at Cleveland State University. It was the 20th debate of the campaign, 10 months to the day after the first.
The race was far different in April 2007, Clinton the front-runner by far. Now Obama holds that place, both in terms of contests and delegates won.
Both Obama and Clinton were on the receiving end of pointed questions from Tim Russert of NBC News, one of two moderators for the event.
Asked whether he was waffling on his pledge of agreeing to take federal funds for the fall campaign, Obama said he was still contesting the primaries.
"If I am the nominee I will sit down with John McCain and make sure we come up with a system that is fair to both sides," he said. Obama could presumably raise far more money than the federal system provides, but accepting government money precludes that.
The equivalent question to Clinton concerned the income tax returns that she and her husband, former President Clinton, file jointly.
"I will release my tax returns," Clinton said, if she becomes the Democratic nominee. She then added she might do so "even earlier," but not before Tuesday's primary.
The two rivals also debated NAFTA, the free trade agreement with Canada and Mexico that is wildly unpopular with blue-collar workers whose votes are critical in any Democratic primary in Ohio.
Neither one said they were ready to withdraw from the agreement, although both said they would use the threat of withdrawal to pressure Mexico to make changes.
"I have said I would renegotiate NAFTA," said Clinton. "I will say to Mexico that we will opt out of NAFTA unless we renegotiate it."
Obama said Clinton has tried to have it both ways, touting the trade deal in farm states where it's popular while finding fault with it in places like Ohio.
"This is something I have been consistent about," said Obama, who said he went to the American Farm Bureau Federation to tout his opposition and used it as an issue in his 2004 Senate campaign.
"That conversation I had with the Farm Bureau, I was not ambivalent at all," said Obama.