Mr Obama said a $700bn (£380bn) package to rescue the US economy was the "final verdict" on eight years of Republican rule.
Mr McCain responded by accusing Mr Obama over his record on finance, saying he had asked for millions of dollars in so-called "earmarks" - money for pet projects - as an Illinois senator.
But both agreed the rescue deal would put massive pressure on the budget of the next president and mean spending cuts.
Senate majority leader Harry Reid said on Saturday morning that members of Congress had made significant progress in their negotiations on the bail-out plan and hoped to be able to announce an agreement in principle on Sunday.
'Piece in the puzzle'
Tens of millions of Americans watched the debate in Oxford, Mississippi, on TV, with only about five weeks to go before the 4 November election.
Last night, John McCain's silence on the middle class was deafening
Sen Joe Biden, Democratic vice-presidential candidate
A telephone poll by CNN and Opinion Research Corp afterwards found 51% said Mr Obama had won, to 38% for Mr McCain.
Obama was widely considered more intelligent, likable and in touch with peoples' problems, and by a slight margin was seen as the stronger leader and more sincere.
A CBS News poll of uncommitted voters meanwhile found that 39% gave Mr Obama victory, 24% thought John McCain had won, and 37% thought it was a dead heat.
Correspondents say this will be seen as an achievement by Mr Obama's team, as foreign policy and national security are considered his rival's strongest topics.
The Illinois senator's campaign manager, David Plouffe, said that the polls showed him making important gains with undecided voters.
Mr Obama was greeted by cheering supporters in Greensboro on Saturday
"We think it's another piece in the puzzle to Senator Obama winning the election," he said.
In a speech on Saturday in Greensboro, North Carolina, Mr Obama said the Republican candidate had proved he was out of touch with the middle class by never once uttering the words during their first debate.
"Through 90 minutes of debate, John McCain had a lot to say about me, but he didn't have anything to say about you," he said. "He didn't even say the words 'middle class.' He didn't even say the words 'working people."'
Mr Obama's running mate, Sen Joe Biden, echoed the comments, saying Mr McCain's judgement on every issue was "wrong".
"Last night, John McCain's silence on the middle class was deafening," he said. "We need more than a brave soldier. We need a wise leader."
The Republican governor of Mississippi, Haley Barbour, said Mr McCain's experience had shone through during the debate.
2 Oct - vice-presidential rivals. Topic: Domestic and foreign policy
7 Oct - presidential contenders. Topic: Any issues raised by members of the audience
15 Oct - presidential contenders. Topic: Domestic and economic policy
The BBC has full and extensive coverage of the debates
"This was real experience. This was someone talking about war, not what they read in a book, what they heard in a lecture," he told the BBC.
In its first post-debate advert, Mr McCain accused his rival of "playing politics, risking lives" when he voted against an Iraq war spending bill in May 2007.
On Friday, the Wall Street journal accidentally ran an advert from the McCain campaign before the debate - and even before he had said he would actually attend - declaring: "McCain wins debate".
The BBC's Allan Little in Oxford says both performances seemed to be sure footed, polished, coherent, focused, meticulously researched.
No-one rambled, nor repeated himself, our correspondent says. Both argued points of policy in detail and with mutual civility, he adds.
During Friday's debate, Sen McCain said he did not need "any on-the-job training".
"I'm ready to go at it right now," he added.
I have a long record and the American people know me very well
Sen John McCain
But Sen Obama said his rival had been "wrong" about invading Iraq and that the war had led the US to take its eye off the ball in Afghanistan, where it should have been pursuing al-Qaeda.
Mr McCain argued that as a result of the "surge" - which involved sending some 30,000 extra US troops to Iraq - US military strategy was succeeding.
"We are winning in Iraq and we will come home with victory and with honour," he said.
Asked about Iran, Mr McCain stressed that Tehran was a threat to the region and, through its interference in Iraq, to US troops deployed there.
He outlined a proposal for a "league of democracies" to push through painful sanctions against Tehran that were presently being blocked in bodies like the United Nations because of opposition from Russia.
Mr McCain also criticised Mr Obama for his previously stated willingness to hold talks with the leaders of Iran without preconditions.
John McCain and Barack Obama on dealing with Iran
Mr Obama rejected that criticism, saying he would reserve the right as president "to meet with anybody at a time and place of my choosing if I think it's going to keep America safe".
However, he said he agreed with his Republican rival that "we cannot tolerate a nuclear Iran" and the threat that that would pose to Israel, a staunch US ally.
Speaking about the so-called war on terror, Mr McCain said he believed the nation was safer than it had been the day after the 11 September 2001 terror attacks but there was still a long way to go.
Mr Obama pointed to the spread of al-Qaeda to some 60 countries and said that the US had to do more to combat that, including improving its own image as a "beacon of light" on rights.
"One of the things I intend to do as president is restore America's standing in the world," Mr Obama said.
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