TEMPE, Ariz. – President Bush and Senator Kerry square off here tonight in their last scheduled debate, a high-stakes duel on domestic policy that may have a decisive impact in the hard-fought contest for the presidency.

“This debate will matter to the outcome. In fact, it could become the pivot point around which the election turns,” a political science professor at Syracuse, Rogan Kersh, said. “It matters a lot.”

While most national polls show Mr. Bush with a narrow lead over Mr. Kerry, the Massachusetts senator appears to enjoy an advantage over Mr. Bush on many of the domestic issues that are to be the subject of tonight’s debate. At campaign stops yesterday in Colorado and Arizona, Mr. Bush sought to close that gap by reminding voters they would ultimately be stuck with the bill for Mr. Kerry’s proposals on health care and education.

“You’re not going to have fiscal sanity if John Kerry is the president,” Mr. Bush said at a fund-raising event in Paradise Valley, Ariz. “Running up the taxes on the American people right now would be bad for our economy. And we’re not going to let him tax you.”

At a rally in Colorado Springs, the president said Mr. Kerry would be unable to keep his promise to limit any tax increases to families making more than $200,000 a year.

“To pay for all the big spending programs he’s outlined during his campaign, he’s going to have to raise your taxes,” Mr. Bush said.

Mr. Kerry spent the day in Santa Fe, N.M., preparing for tonight’s encounter. He had no public speeches but was seen briefly as he took a bicycle ride around town.

Both campaigns took to the airwaves yesterday with new television ads addressing concerns about fast-rising health-care costs and the growing ranks of uninsured.

The Kerry campaign’s spot accuses Mr. Bush of being in the pocket of the major pharmaceutical companies. In the ad, the Massachusetts senator says, “For the last four years, one man has stood between America and lower cost prescription drugs: George Bush.” Mr. Kerry also criticizes Mr. Bush for supporting legislation that bars Medicare from negotiating drug prices with manufacturers.

The Bush ad suggests that Mr. Kerry’s plans to broaden health-insurance coverage would result in a government takeover of the health-care system.

The ad shows a diagram of a Byzantine array of government agencies that it suggests would be involved in implementing Mr. Kerry’s proposal. “Rationing. Less access. Fewer choices. Long waits. And Washington bureaucrats, not your doctor, make final decisions on your health,” the ad’s narrator declares.

Aides to Mr. Kerry angrily denounced the Bush campaign’s commercial as inaccurate.

“The president knows that these ads he launched today on health care are utterly false and completely dishonest,” said a senior Kerry adviser, Tad Devine.

A health-policy expert for Mr. Kerry, Christopher Jennings, said Republicans were incorrectly implying that the Democrat’s proposal for health insurance is similar to the plan proposed by President Clinton early in his first term.

“It couldn’t be any more substantively different,” said Mr. Jennings, who was also an adviser to Mr. Clinton. “This is the right-wing, cookie-cutter charge.”

Mr. Jennings described Mr. Clinton’s plan as “a much more aggressive and government-oriented policy.”

Senator Frist of Tennessee defended the Bush campaign’s critique. The Senate majority leader said the Kerry plan would add nearly 22 million Americans to the federally financed Medicaid program.

“Just ask any physician or any hospital what happens when a patient is treated in Medicaid,” said Mr. Frist, who is a heart surgeon. “Prices are strictly controlled. Ultimately there is rationing.”

The Syracuse professor, Mr. Kersh, said Mr. Bush has a tougher task in the debate.

“Bush has,at the same time,to appeal to people who want new spending on health care and somehow also convince a big chunk of his own base that he’s not going to continue these kinds of profligate budgets,” Mr. Kersh said. “He’s got to perform something of a tightrope act.”

Meanwhile, an Arizona judge rejected yesterday a last-minute bid by the state Libertarian Party to block the debate because the Libertarian presidential nominee, Michael Badnarik, was not invited to participate.

At an hour-long hearing in a Phoenix courtroom, an attorney representing the Libertarians, David Euchner, tried to convince Judge F. Pendleton Gaines III that Arizona State University was favoring the Democratic and Republican parties by serving as host for a debate that excludes Mr. Badnarik, who is on the ballot here and in 47 other states.

“They’re using our money to come to Arizona and communicate their ideas,” Mr. Euchner complained. “They’re coming into our house – the Arizona taxpayers – and asking us to pay the bill.”

The Libertarians’ argument centered on a provision in the Arizona Constitution that prohibits gifts of public resources to individuals or private organizations. Past court rulings have held the clause is implicated only when the public doesn’t benefit from the expenditure.

Lawyers for the organization that has sponsored all major presidential debates since 1988, the Commission on Presidential Debates, denied that it is a tool of the major parties.

“It is independent of any political party,” the commission’s general counsel, Lewis Loss, said via a speakerphone link from Washington.

Mr. Loss said the commission applies nonpartisan criteria to select the candidates for each debate. The main hurdle is that a candidate must have at least 15% support in five national opinion polls. Mr. Loss noted that in 1992 independent candidate Ross Perot debated after meeting that test.

Mr. Loss also told the judge that if Mr. Badnarik was added to the mix, Messrs. Bush and Kerry were likely to withdraw from the debate.

“It is unlikely in the extreme that they would simply agree to proceed tomorrow evening in what would be a radically changed debate,” Mr. Loss said.

“What we have here is a de minimis amount of public money being expended for an enormous public benefit,” said a local attorney for the debate commission, Glen Hallman.

The university has said it has raised private funds to cover all but about $200,000 of the estimated cost of the debate, $2.5 million. An Arizona assistant attorney general who represented the school at yesterday’s hearing, Carrie Brennan, said the debate would result in a bonanza of good publicity for the school, the city of Tempe, and the state.

“This is the biggest event in Arizona politics since Barry Goldwater ran in 1964,” Ms. Brennan told the court. “It has an educational purpose.”

Mr. Euchner scoffed at the suggestion that the debate commission is nonpartisan. “The commission was founded by the Democratic National Committee and the Republican National Committee,” he said.

Judge Gaines suggested that any de bate involving the presidential candidates, even just two of them, could strengthen civic ideals.

“Why do you think it wouldn’t be a public purpose for the university to encourage a kind of Jeffersonian dialogue?” he asked.

“It’s not a Jeffersonian dialogue,” Mr. Euchner replied.

Mr. Euchner also cited surveys suggesting that up to 68% of the electorate want third-party candidates included in the debates. “All the polls are showing that voters are sick of seeing two people on the stage,” he said. “They don’t want an infomercial.”

Mr. Euchner rejected a suggestion by an opposing attorney that admitting Mr. Badnarik to the debate would lead to a “mob scene” of minor candidates on stage.

“During the primary season you could have 10 Democrats and 10 Republicans on stage and it’s not a mob scene,” Mr. Euchner said.

In the end, the judge found that the Libertarians’ case was not strong enough to justify an injunction.

“Based on everything I’ve heard this morning, I do not find there’s a probability of success on the merits,” Judge Gaines said as the hearing concluded. He also said he was “troubled very much” that the Libertarians waited so long to bring their challenge.

While the judge refused to stop the debate or to force Mr. Badnarik on stage, he said the Libertarians could pursue the lawsuit to seek the recovery of any tax money that may have been improperly spent. He also buoyed the hopes of some in the Libertarian camp by saying Mr. Euchner’s arguments on that point “may have some merit.”

As the lawyers presented their arguments, Judge Gaines also displayed a sense of humor.

While discussing the extensive security arrangements for the debates, Mr. Euchner said to the court, “We don’t want the president to be assassinated.”

The judge shot back, “I assume some people wouldn’t even want John Kerry to be assassinated.”

Mr. Euchner said later that the Libertarians decided not to appeal because they believed they had a slim chance of getting a higher court to overturn the judge’s decision. The Libertarians plan to press their case to ensure that all costs of the debate are borne by private entities. They also took some solace in what they saw as a concession by the debate commission’s lawyer that Messrs. Bush and Kerry are afraid to face a third-party challenger.

“If the judge had ordered Badnarik on that stage, Bush and Kerry would have ran for the hills,” Mr. Euchner said.