Iraq and terrorism dominated a hard-hitting and sometimes personal debate Tuesday night between the vice presidential nominees, with Vice President Cheney accusing the Democratic ticket of lacking the judgment to lead, and Sen. John Edwards (N.C.) responding that Cheney and President Bush lack credibility.

The lines of attack were drawn in the opening moments of the nationally televised encounter at Case Western Reserve University, with Cheney asserting strongly that the decision to topple Saddam Hussein last year was justified by an "established Iraqi track record with terror."

Striking an incredulous air at Cheney's claim, Edwards responded, "Mr. Vice President, you are still not being straight with the American people."

This set the tone for the 90-minute debate, which featured equally sharp, sometimes snappish exchanges as it turned to such matters as the state of the economy, taxes, tort reform and same-sex marriage.

Cheney rapped Edwards's one term in the Senate, dismissing it as "not very distinguished" and marked by chronic absenteeism, and Edwards fired back with a review of Cheney's record as a congressman in the 1980s.

Noting that as vice president he presides over the Senate, Cheney said acerbically to the freshman senator, "The first time I met you is when you walked on the stage tonight." Cheney met Edwards twice before, according to the Kerry-Edwards campaign, which e-mailed reporters a photograph.

In defense, Edwards shot back, "I'm surprised to hear him talk about records," and pivoted into a discussion of conservative votes cast by Cheney. "He voted against the Department of Education. He voted against funding for Meals on Wheels for seniors. He voted against a holiday for Martin Luther King. He voted against a resolution calling for the release of Nelson Mandela in South Africa."

While this peevish exchange turned on somewhat arcane details, in general the candidates engaged in a broad way with the major questions facing the electorate in the Nov. 2 contest between Bush and Democratic nominee John F. Kerry. They clashed over whether circumstances are improving or worsening in Iraq, and whether the United States is on the upswing from Bush's policies or is still stalled in a way that has left more people jobless or struggling to deal with rising health costs.

Historically, vice presidential debates have not figured prominently in general elections, but both campaigns said Cheney's central role in the administration and the tightening contest between Bush and Kerry could make this one an exception.

No matter the electoral implications, the evening lived up to its advance billing as a vivid display of two politicians with widely divergent personal styles, public records and political philosophies. Cheney spoke without inflection, rarely flashed smiles and often looked down during his answers. Edwards struck a smiling, conversational tone, but there was nothing amiable in his case against Cheney. Repeatedly, he assailed the vice president's truthfulness and his record as chief executive of the controversy-plagued Halliburton Corp.

The most personally intimate exchange of the evening came when moderator Gwen Ifill of PBS asked Cheney, who has a gay daughter, about the administration's support of a proposed constitutional ban on same-sex marriage. As he had answered four years ago, he said that the issue should be in the hands of the states, not the federal government, but that the president sets policy for the administration.

In responding, Edwards said: "I think the vice president and his wife love their daughter. I think they love her very much. And you can't have anything but respect for the fact that they're willing to talk about the fact that they have a gay daughter, the fact that they embrace her. It's a wonderful thing."

But then his message became more pointed: "We should not use the Constitution to divide this country. . . . This is using the Constitution as a political tool, and it's wrong."

Cheney on a number of occasions chose not to respond in depth to detailed attacks from Edwards, even brushing aside as "a smoke screen" a strong Edwards statement on Cheney's connection to Halliburton and its alleged use of overseas tax havens and no-bid contracts in the reconstruction of Iraq.

"The facts are the vice president's company that he was CEO of, that did business with sworn enemies of the United States, paid millions of dollars in fines for providing false financial information, it's under investigation for bribing foreign officials," Edwards said. Cheney merely referred the American people to a Web site to check the facts.

By contrast, when Edwards was pressed about his record as a trial lawyer -- a potentially touchy area for him -- he launched a detailed defense, invoking one of his most emotional cases. "We want to put more responsibility on the lawyers to have the case reviewed by independent experts to determine if the case is serious and meritorious before it can be filed," he said. "But we don't believe that we should take away the right of people like Valerie Lakey, who was the young girl who I represented, 5 years old, severely injured for life on a defective swimming pool drain cover."

Edwards was primed to deflect attention away from suggestions that he lacks experience by attacking Cheney's resume. "The vice president and president like to talk about their experience on the campaign trail. Millions of people have lost their jobs. Millions have fallen into poverty. Family incomes are down, while the cost of everything is going up. Medical costs are up the highest. . . . We have this mess in Iraq. Mr. Vice President, I don't think the country can take four more years of this kind of experience."

Edwards was determined to pull the discussion to domestic issues such as the economy, jobs and health care. When Cheney segued from a specific question about jobs with a paean to education and business development, Edwards sarcastically quipped to the moderator, "Your question was about jobs?"

"In the time that they have been in office . . . 1.6 million private-sector jobs have been lost, 2.7 million manufacturing jobs have been lost," Edwards said. Cheney defended the administration's record, saying: "We've got 111 million American taxpayers that have benefited from our income tax cuts. We've got 33 million students who've benefited from No Child Left Behind. We've got 40 million seniors who benefited from the reform of the Medicare system. The Democrats promised prescription drug benefits. For years they've run on that platform. They never got it done. The president got it done."

On national security, much of Cheney's attack echoed the lines the GOP ticket has struck for months: that Kerry and Edwards lack the consistency and resolve to effectively fight terrorism.

"You're not credible on Iraq because of the enormous inconsistencies that John Kerry and you have cited time after time after time during the course of the campaign," Cheney said. "Whatever the political pressures of the moment requires, that's where you're at. But you've not been consistent, and there's no indication at all that John Kerry has the conviction to successfully carry through on the war on terror."

Edwards called that a "complete distortion."

"The American people saw John Kerry on Thursday night" during the first presidential debate last week at the University of Miami, he said. "They don't need the vice president or the president to tell them what they saw."

That remark hinted at Cheney's and Edwards's goals for the night. Cheney was hoping to reverse what Republicans acknowledge was Kerry's success at putting Bush on the defensive, and Edwards was trying to help the ticket make the last month of the race be about Bush's record rather than Kerry's record of Iraq votes and statements.

In this battle to steer conversation to their preferred terrain, the men sparred over who is most and least committed to building the nation's defenses, with Cheney saving his harshest assessment for Kerry. "When he ran for the Senate he opposed, or called for the elimination of, a great many major weapons systems that were crucial to winning the Cold War and are important today to our overall forces," Cheney said.

Edwards responded: "This vice president, when he was secretary of defense, cut over 80 weapons systems, including the very ones he's criticizing John Kerry for voting against. These are weapons systems, a big chunk of which, the vice president himself suggested we get rid of after the Cold War. The reality is that John Kerry has consistently supported the very men that he served with in Vietnam and led."

Former Iraqi administrator L. Paul Bremer's comments Monday that the Iraq occupation needed more troops at the beginning set the stage for several exchanges. Edwards called it representative of misjudgments that have left the United States picking up 90 percent of the cost of the Iraq invasion and 90 percent of the casualties.

Cheney struck an indignant tone in response, saying that this figure did not take into account the efforts of the Iraqis: "He won't count the sacrifice and the contribution of Iraqi allies. It's their country. They're in the fight. They're increasingly the ones out there putting their necks on the line. . . . And for you to demean their sacrifices strikes me as . . ."

"Oh, I'm not," Edwards interjected. "I'm not demeaning."

Edwards, echoing Kerry's remarks from the first debate, said, "The reality you and George Bush continue to tell people, first, that things are going well in Iraq -- the American people don't need us to explain this to them; they see it on their television every single day. We lost more troops in September than we lost in August, lost more in August than we lost in July, lost more in July than we lost in June."

For all the differences, the format was calculated to keep the fireworks subdued. At the insistence of the Bush campaign's debate negotiators, the encounter took place with both men seated at a table. Republicans feared that a standing format would give Edwards a greater ability to summon the dramatic techniques he employed in the courtroom. The two men shook hands as they took the stage, but, by agreement, not once the debate began at 9 p.m. For five minutes before the questioning began, they sat stonily at the table, saying nothing to each other.

Vice President Cheney and Democratic vice presidential candidate John Edwards shake hands before their debate at Case Western Reserve University in Cleveland. Moderator Gwen Ifill of PBS is in the foreground.John Edwards, the Democratic vice presidential candidate, responds to Vice President Cheney during their debate in Cleveland.Vice President Cheney, left, and Democratic challenger John Edwards disagree over the United States' Iraq policies.

Vice President Cheney and Democratic challenger John Edwards shake hands before facing off in Cleveland.