Democrats eyeing the Oval Office held their first major debate at the University of New Mexico Thursday, and seemed to find common ground amid their disagreements – they all blasted President Bush on Iraq and the economy.

While welcoming the president's decision to finally seek the United Nations' help in getting Iraq under control, the candidates contended that he should have done it earlier. His delay, they said, has imperiled U.S. relations worldwide. 

Now Bush must "go back to the very people he humiliated," said former Vermont Gov. Howard Dean (search), who by the luck of the draw was asked the opening question at the televised debate.

Sen. John Kerry (search) of Massachusetts said that "the swagger of a president who says 'bring 'em on' does not bring our troops peace or safety."

And former House Democratic Leader Dick Gephardt (search) of Missouri said, "We have a president who has broken up alliances that Democratic and Republican presidents have put together over 70 years."

The event featuring eight of the nine presidential hopefuls took place on the tail end of candidate Dean's summer surge, which many of his rivals were hoping to quash. But their focus on Bush, and not on each other, could mean that Dean will remain the front-runner.

Al Sharpton (search) was delayed in New York by poor weather and could not participate in the debate.

Sharing a University of New Mexico stage with Dean, Kerry and Gephardt were Sens. Joe Lieberman (search) of Connecticut, John Edwards (search) of North Carolina, Bob Graham (search) of Florida, Rep. Dennis Kucinich (search) of Ohio and former Illinois Sen. Carol Moseley Braun (search).

Braun, the only woman candidate, argued that Operation Iraqi Freedom represented a wrong turn in the war on terror. After reminding the audience that the United States still hadn't tracked down Usama bin Laden (search), she said: "We haven't been looking for him because we got off on the wrong track (in Iraq)."

Lieberman, who like Gephardt supported the war with Iraq early on, said he would send more U.S. troops to help safeguard those there now.

Graham, the only senator seeking the nomination who voted against the Iraq war resolution last fall, said he voted that way because "I thought it was the wrong war against the wrong enemy."

Graham said that, despite his consistent opposition to the war, he would support the administration's request for an estimated $60 billion to $70 billion to help cover continuing costs.

"We have an obligation to support those troops," Graham said.

The contenders were also asked about proposals to overhaul immigration laws, particularly to allow the estimated 3 million undocumented immigrants from Mexico to remain in the United States. Relaxing current law drew broad support from the Democratic rivals.

"This country is a melting pot, a fabric," Gephardt said.

"Immigration for me is not just another issue. It's me, it's my family," said Lieberman, noting that his ancestors, like those of most Americans, had come from overseas.

"He (Bush) has used 9-11 as an excuse for not doing what he promised to do in reforming immigration laws," Lieberman added.

Hispanics, who number 38.8 million according to the latest census, represent about 7 percent of the voting population nationwide. In 2000, about 7.5 million Hispanics were registered to vote.

On the economic front, the Democrats criticized Bush's tax cuts and suggested that the number of U.S. jobs decreased as a result of his policies.

Edwards also suggested that Bush's attempts to woo Hispanic voters were ultimately a series of empty gestures.

"The president goes around the country speaking Spanish. The only Spanish he speaks when it comes to jobs is hasta la vista," Edwards said, borrowing a line made famous by actor and California GOP gubernatorial candidate Arnold Schwarzenegger.

The candidates did argue on trade and on tax policies, sparring briefly over whether their respective positions on trade agreements would protect workers' rights and environmental standards.

Gephardt, who counts organized labor as a crucial constituency, continued his attack on his rivals for supporting free-trade pacts.

Several of the Democratic contenders promote rolling back Bush tax cuts. Lieberman, however, said he disagreed "with Governor Dean and others" who advocate undoing the full Bush tax plan to fund other priorities, including universal health care coverage. Gephardt has also called for such a repeal.

Lieberman advocated undoing only those cuts that fattened the wallets of upper-income taxpayers. He suggested the health insurance plans supported by Dean and Gephardt cost too much.

"Why would we want to keep anything of the Bush tax plan?" asked Gephardt in response. "It's a miserable failure." It wasn't the only time Gephardt used that phrase; on another occasion he said, "this president is a miserable failure," implying Bush had botched every aspect of the job.

The gathering was broadcast live on public television with a Spanish translation available and also will be aired Saturday on Univision, the nation's largest Spanish-language network, in a nod to the rising influence of Hispanic voters. New Mexico has a large Hispanic population — about 42 percent — and a Hispanic governor, Democrat Bill Richardson (search).

Richardson, who gave opening remarks at the debate, challenged "Hispanics across the country to mobilize and energize our communities for next year's election."

The event was moderated by PBS correspondent Ray Suarez and Univision anchor Maria Elena Salinas.

The Associated Press contributed to this report.