LAS VEGAS (AP) – John Edwards said Saturday he will definitely stay in the presidential race, trying to reassure voters and donors that he can handle the dual pressure of the campaign and his wife’s cancer diagnosis.

At a Democratic presidential forum focused on health care, Mr. Edwards pressed his rivals to provide a detailed plan to cover the nation’s uninsured – estimated at about 47 million – and describe how they will pay for it. His chief competitors, Senators Clinton of New York and Obama of Illinois, did not rule out the possibility that they would follow his lead with a plan requiring a tax increase, but they provided no specifics.

“I have not foreclosed the possibility that we might need additional revenue in order to achieve my goal, but we shouldn’t underestimate the amount of money that can be saved in the existing system,” Mr. Obama said when asked whether he would raise taxes to reach his goal of universal coverage by the end of his first term.

“I can tell you I will do whatever it takes,” the Illinois senator added.

Mrs. Clinton did not say whether or not she is considering a tax increase, but said she cannot see putting more money into what she described as a current broken system. She said she is committed to succeeding where she failed with the health care plan she crafted in her husband’s first term in the White House.

“We’re going to change the way we finance the system by taking away money from people who are doing well now,” said Mrs. Clinton. Asked who she was referring to, she mentioned insurance companies.

The forum was sponsored by the Service Employees International Union and the Center for American Progress Action Fund, a Washington-based policy group.

It came two days after Mr. Edwards announced that the breast cancer that his wife thought she had beaten had returned, this time in her bone. He pointed out his wife, Elizabeth, sitting in the front row and said they both understand that dealing with their personal struggle will require “a focus and a maturity.”

“I’m definitely in the race for the duration,” he said. “This is not the first challenge that Elizabeth and I have been through.”

Mr. Edwards pointed out that they lost their teenage son, Wade, 11 years ago in a car accident – something that he didn’t talk about much when he ran for president four years ago.

“I know because of the nature of the woman I’m married to that she will be there every single step of the way,” he said. “We take our responsibility to serving this country very seriously.”

Mr. Edwards said he and his wife are getting too much credit for forging ahead when millions of women are enduring the same struggle and the additional worry of getting the necessary care.

“One of the reasons that I want to be president of the United States is to make sure that every woman and every person in America gets the same things that we have,” Mr. Edwards said. His plan would require employers to provide insurance and individuals to have it at a cost of $90 billion to $120 billion.

Mr. Edwards said any politicians who say they can provide universal health care and other promises while ending the federal deficit are not being honest.

Mr. Edwards said any politician who says they can provide universal health care and other promises while ending the federal deficit are not being honest.

“They’ve probably got a bridge in Brooklyn they want to sell you, too,” Mr. Edwards said to laughter and applause. “I just don’t think it can be done.”

No other candidate has given a cost estimate. Bill Richardson, the Governor of New Mexico, however, said he could provide universal care in his first year as president without raising taxes.

Mr. Richardson said his plan would include a tax credit for low-income people who need coverage and prevention strategies such as a nationwide smoking ban like the one he signed in New Mexico. He said he would pay for his plan in large part by ending the war in Iraq and shifting the military spending to human needs – an idea that won loud applause.

Senator Dodd of Connecticut said his plan would require a tax increase by repealing President Bush’s cuts to the top 2 percent of income-earners.

Video of the candidate forum was fed live over the Internet. The moderator, Time magazine’s Karen Tumulty, took questions from Internet viewers as well as prescreened questions from union members in the audience.

Representative Dennis Kucinich of Ohio and Mike Gravel, a former Senator from Alaska, promoted a single-payer universal health care system.

Mr. Obama was challenged by an audience member who said she had gone to the senator’s Web site looking for health care reform information and found only plans about HIV and lead poisoning. He said he would have a detailed plan in a couple months, after he has a chance to discuss it further with experts and front-line workers.

He said he wants to require that employers either provide coverage or help their workers pay to get their own and favors cutting costs through prevention, management and technology improvements.

Mrs. Clinton, who received the warmest reception from the audience with several interruptions for applause, said her deadline for universal health care would be two terms in office. She said part of the reason her plan failed in the early 1990s was that people with coverage did not understand that it would not change. “We’re going to do a better job explaining this time,” she said.

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Associated Press writer Nedra Pickler in Washington contributed to this report.