They debated head-to-head after John Edwards withdrew from the race.Both refused to rule out the idea of running for office as presidential candidate and running mate.
Mr Obama has seen his campaign funds swell since the start of the year, with $32m of contributions reported in January.He is now running TV advertisements in 20 of the states which will be voting in primaries on Tuesday.
His opponent has yet to release figures for the past month, but the Clinton campaign says it raised 26.8m in the last three months of 2007.
Mr Obama said the US was facing a "defining moment", opening the debate in the Kodak theatre in Los Angeles, venue for the Oscars ceremony.
"What is at stake right now is whether we are looking backwards or whether we are looking forwards. I think it is the past versus the future."Mrs Clinton said that the Republican administration of President George W Bush had created a "stack of problems".
"It is imperative that we have a president, starting on day one, who can begin to solve our problems," she said.The debate was mostly cordial in tone.
"I was friends with Hillary Clinton before we started this campaign; I will be friends with Hillary Clinton after this campaign is over," said Mr Obama.Mrs Clinton noted that "the differences between Barack and I pale in comparison to the differences that we have with Republicans".
But there were also moments of tension, including during a discussion about the Iraq war.Mrs Clinton defended her decision to vote in October 2002 to allow President Bush to use force in Iraq, saying she had made a "reasoned judgement" based on the information the president had set out to the nation.
"It was a sincere vote based on my assessment at the time and what I believed he would do with the authority he was given," she said.She also said that she had "the necessary credentials and gravitas" to lead the country in a withdrawal from Iraq without endangering US forces or further destabilizing the area.
Mr Obama responded: "Senator Clinton mentioned the issue of gravitas and judgment. I think it is much easier for us to have the argument when we have a nominee who says `I always thought this was a bad idea. This was a bad strategy.' It was not just a problem of execution."
Another pointed exchange came on the subject of whether illegal immigrants should be able to obtain driver's licences.Mr Obama supports such a policy while Mrs Clinton at first backed it and now opposes it.
"Senator Clinton gave a number of different answers over the course of six weeks on this," Mr Obama said, turning to Mrs Clinton.She called the controversy "a diversion" from efforts to come up with comprehensive immigration reform."I sponsored immigration reform before Barack came to the Senate," she said.
In the Republican race, California Governor Arnold Schwarzenegger added his support to John McCain's bid.Rudy Giuliani, who pulled out of the Republican contest this week, has also said he is backing Mr McCain.
It is thought that Mr Schwarzenegger's backing may improve Mr McCain's chances of winning the California primary - one of the many to be held on Super Tuesday.The Republicans held their own televised debate on Wednesday night.
It was dominated by verbal jousting between Mr Romney and Mr McCain, with the two others in the race - Mike Huckabee and Ron Paul, who are both trailing - struggling to be heard.