"What is important is that we understand exactly the challenges facing us in order to defeat [Republican Sen. John] McCain," Clinton said, although she did say she also thought Obama could win in the fall.
But Obama pushed back with vigor, saying voters care more about a candidate who can improve their lives. He also complained about minor missteps dominating too much of the race.
"I think what's important is to make sure that we don't get so obsessed with gaffes that we lose sight of the fact that this is a defining moment in our history," Obama said. "We are going to be tackling some of the biggest issues that any president has dealt with in the last 40 years."
The 90-minute debate, broadcast by ABC News, was the first in two months.
The candidates are locked in an increasingly tight battle - this week's Daily News/Franklin & Marshall poll showed Clinton leading in Pennsylvania by just 6 points.
Gaffe-obsession dominated the early part of the debate as Obama took a lot of heat, fielding questions about his former Chicago pastor, Rev. Jeremiah Wright; about his recent statements about small-town Americans' being "bitter," and about why he doesn't wear an American flag pin.
More than once Obama said he thought small things get overhyped along the trail.
On the flag pin, he noted, "This is the kind of manufactured issue that our politics has become obsessed with and, once again, distracts us from what should be my job when I'm commander in chief, which is going to be figuring out how we get our troops out of Iraq and how we actually make our economy better for the American people."
One issue raised last night, which hasn't been covered much by the mainstream press, was Obama's relationship with 1960s radical Bill Ayers, a member of the Weather Underground, a radical group that claimed responsibility for a dozen bombings between 1970 and 1974.
Ayers - who served on the board of an anti-poverty organization with Obama - told the New York Times in 2001, "I don't regret setting bombs . . . I feel we didn't do enough."
Obama said Ayers "engaged in detestable acts 40 years ago when I was 8 years old." He stressed that the two were not close, but added that questions about the relationship were a distraction.
"This kind of game, in which anybody who I know, regardless of how flimsy the relationship is, that somehow their ideas could be attributed to me, I think the American people are smarter than that," he said.
Clinton criticized Ayers' statements and said, "This is an issue that certainly the Republicans will be raising."
To that, Obama noted that Clinton herself was vulnerable to criticism, because President Bill Clinton commuted the sentences of two members of the Weather Underground group, "which I think is a slightly more significant act than me serving on a board with somebody for actions that he did 40 years ago."
Clinton was asked about her now-infamous statements about landing in Bosnia amidst sniper fire in 1995.
In the second half of the debate, Gibson and Stephanopoulos finally got around to substance, asking about social security, gasoline prices, Iraq, affirmative action, taxes and gun control.
Clinton criticized Obama's willingness to raise the ceiling above which income is exempt from social security taxes.
Obama said Clinton was refusing to acknowledge that some sacrifices will be necessary to address the social security problem, saying Clinton acted as if there were a "magic solution" to the problem.
"You can't get something for nothing, and if we care about social security . . . then we have an obligation to figure out how to stabilize the system." he said.
On rising gasoline prices, Clinton appeared to be willing to entertain a suspension of the federal gas tax, which Republican John McCain has recommended, saying, "If it reaches four dollars a gallon, people won't be able to drive to work." She said if that were done, she would favor a windfall profits tax.
Obama said "the only way to reduce prices is to reduce demand," and he repeated his call for a Manhattan Project to develop alternative energy.
Both repeated pledges to bring troops home from Iraq.
Asked about affirmative-action policies at universities, Obama said students' economic backgrounds should be considered.
"So if they look at my child, and they say, 'You know, Malia and Sasha, they've had a pretty good deal,' then [race] shouldn't be factored in.
"On the other hand, if there's a young white person who has been working hard, struggling, and has overcome great odds, that's something that should be taken into account.
"So I still believe in affirmative action as a means of overcoming both historic and potentially current discrimination, but I think that it can't be a quota system and it can't be something that is simply applied without looking at the whole person, whether that person is black, or white, or Hispanic, male or female," he said.
Clinton also said students from different backgrounds should get aid.
"Well, here's the way I'd prefer to think about it. I think we've got to have affirmative action generally to try to give more opportunities to young people from disadvantaged backgrounds, whoever they are."
On taxes, Clinton pledged to not raise taxes for people making less that $250,000 a year. Obama said he would provide tax cuts for people making less than $75,000. He also said he would not raise taxes for the middle class, but did not give an exact cut-off number, saying it would be between $200,000 and $250,000.
Asked about gun control, both candidates were cautious. Clinton noted a recent appearance in West Philadelphia, where she unveiled a crime plan that would include more funding for police. She also said she supported a return of the assault-weapons ban. But she stressed that she respected the rights of lawful gun owners.
Obama also said he supported laws that would stem the tide of illegal guns in cities, and also stressed his support for lawful gun owners. *