Five days before Super Tuesday, the two alternated between civility and pointed swipes, underscoring the importance of the upcoming contests. The debate came as Obama's campaign reported raising a staggering $32 million in January, cash aplenty to advertise all through the nearly two dozen upcoming races from coast to coast - and contests beyond.
Clinton's campaign reported raising $26.8 million from October through December, the most recent period she reported.
Clinton defended the increasingly high-profile role of her husband, former President Clinton, in her campaign and his recent sharp criticism of Obama. "At the end of the day, it's my name that is on the ballot."
Both were asked about the possibility of a "dream ticket" of Clinton-Obama - or Obama-Clinton.
"Obviously there's a big difference between those two," Obama said. "I respect Senator Clinton, I think her service to this country is extraordinary." But he said, "We've got a lot more road to travel" before such a decision.
Clinton agreed it was too early to discuss running mates.
Both predicted that one of them would be the next president in a history-making inaugural. Obama would be the first black president, Clinton the first female president.
Clinton said the Republicans are "more of the same" and, gesturing toward Obama, she said, "We will change our country."
Making amends for his apparent snub of her at Monday's State of the Union Address, Obama assisted Clinton by pulling back her chair as the debate - televised on CNN - began and ended. They then embraced.
But it wasn't all sweetness and light.
One of their most pointed exchanges came on the question of whether illegal immigrants should be able to obtain driver's licenses. Obama supports doing so; Clinton initially supported it and now opposes it.
"Senator Clinton gave a number of different answers over the course of six weeks on this," Obama said, turning to Clinton. "Initially, you said you were for it, then you said you were against it." He said he was raising her wavering to underscore that it is "a difficult political issue."
Clinton called the controversy "a diversion" from efforts to come up with comprehensive immigration reform. "I co-sponsored immigration reform in 2004 before Barack came to the Senate," she said.
Obama argued for his candidacy, saying, "I respect Senator Clinton's record. I think it's a terrific record. But I also believe that the skills that I have are the ones that are needed right now to move the country forward, otherwise I wouldn't be running for president."
They also clashed on Iraq.
Clinton suggested only she had "the necessary credentials and gravitas" to lead the country in withdrawing from Iraq without endangering U.S. forces or further destabilizing the region. She said it was crucial to bring Syria and Iran to the diplomatic table.
Obama shot back, "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."
Clinton voted in October 2002 to authorize President Bush to use force in Iraq, while Obama opposed such authority in a speech he gave in 2002 as a member of the Illinois state Senate.
The two also reached out quickly to backers of former rival John Edwards, who bowed out of the race Wednesday without endorsing either one. Both praised his efforts in their opening statements.
Obama called Edwards "a voice for this party and this country for many years to come." Clinton saluted both Edwards and his wife, Elizabeth, as setting "their personal example of courage and leadership" in their advocacy for the poor.
Asked whether it was good for the country to have another Clinton in the White House, further extending Bush and Clinton family control over government, Clinton drew applause in the Kodak Theatre - home of the Academy Awards - when she replied, "It did take a Clinton to clean after the first Bush and I think it might take another one to clean up after the second Bush."
The nation's weakening economy was a prime topic, and both candidates said they preferred Democratic-proposed stimulus plans that would give more tax relief to low- and middle-income workers than would Republican proposals.
Obama focused on Republican front-runner John McCain, praising McCain's two votes against Bush's first-term tax cuts and questioning his support now for extending them. "Somewhere along the line, the Straight Talk Express lost some wheels," the Illinois senator said, referring to the name of McCain's campaign bus.
Both Obama and Clinton nodded in agreement as they compared Democratic economic solutions to those put forward by the GOP.
Befitting a Hollywood audience, among the celebrities in the theater were Diane Keaton, Jason Alexander, Pierce Brosnan, Rob Reiner, Stevie Wonder, Kate Capshaw, Steven Spielberg, Leonardo DiCaprio, Bradley Whitford and Gary Shandling.
Both candidates acknowledged policy differences but also sought to ratchet back what had become increasingly personal attacks and the animosity of their last debate before the Jan. 26 South Carolina primary, which Obama won by a margin of 2-to-1.
Obama appears to have most of the momentum as of now, including high-profile endorsements and impressive fundraising. But Clinton has considerable institutional strength and is still widely favored to do better overall than Obama on Super Tuesday.
"I was friends with Hillary Clinton before we started this campaign. I will be friends with Hillary Clinton after this campaign is over," Obama said .
"We're having a wonderful time," Clinton said at one point.
