HEMPSTEAD, New York — John McCain, needing to reignite his faltering presidential campaign, accused Barack Obama in their final debate of waging class warfare with his tax plans and lashed out at the Democrat’s efforts to link him to George W. Bush’s unpopular presidency.

“Senator Obama, I am not President Bush. If you wanted to run against President Bush, you should have run four years ago,” McCain said.

McCain came out fighting Wednesday night in what was perhaps his last big opportunity to turn around a campaign less than three weeks before the election, but Obama emerged from the encounter relatively unscathed.

McCain’s poll numbers have fallen as Americans appear increasingly unwilling to put another Republican in the White House at a time of financial turmoil and fears of a recession. Major U.S. stock market indexes fell nearly 8 percent or more Wednesday.

The 90-minute encounter, at Hofstra University outside New York City, had the fireworks lacking in the candidates’ first two debates. With the rivals seated at a round table, McCain assailed Obama’s character and his campaign positions on taxes, trade, abortion and other issues.

McCain heatedly demanded that Obama explain his relationship with William Ayers, a Vietnam war-era radical. Obama brushed off the attack, saying he was 8 years old when Ayers was involved in anti-war activities, including the bombing of federal buildings.

For all of McCain’s intensity, it was far from clear that he managed to undermine Obama’s growing popularity. The attacks also risked a backlash: Polls have shown that personal attacks by the McCain campaign — including advertisements about Ayers — have backfired, alienating voters at a time that the economy is the overwhelming concern.

When McCain talked about Ayers, Obama countered: “The fact that this has become such an important part of your campaign, Senator McCain, says more about your campaign than it says about me.”

As in the previous two debates, national polls showed a majority of debate watchers rated Obama the clear winner. A CNN/Opinion Research Corp. poll found that 58 percent of those surveyed said Obama did the best job in the debate, with 31 percent saying McCain did better. The poll was conducted by telephone with 620 adult Americans who watched the debate and had a sampling error of plus or minus 4 percentage points.

Obama lacked McCain’s intensity, as he looked to maintain a calm, confident, presidential demeanor and avoid mistakes that could undermine his lead. But he also leveled a few accusations of his own.

“One hundred percent, John, of your ads, 100 percent of them have been negative,” Obama said.

“It’s not true,” McCain retorted.

“It absolutely is true,” said Obama, seeking the last word.

McCain is currently running all negative ads, according to a study by the University of Wisconsin-Madison. But he has run a number of positive ads during the campaign.

Obama, seeking to become the first black U.S. president, went into the debate ahead not only in national polls, but in surveys of most of the swing states crucial for victory. He has more money to spend than McCain and has organized a massive effort to get out the vote on Nov. 4.

With few exceptions, the campaign is being waged in states that voted Republican in 2004 — Virginia, Colorado, Iowa — and in many of them, Obama holds a lead in the polls.

McCain, a veteran senator and former Vietnam prisoner of war, has struggled as his campaign themes repeatedly changed: focusing on his experience, then his maverick reputation and, then to attacks on Obama’s character. His choice of Sarah Palin, the conservative Alaska governor, has delighted many Republicans, but appears to have alienated vital independent voters.

But an Obama victory is not assured. He has built up his lead only in recent weeks as the financial crisis has worsened and his lead, single digits in some polls, is hardly insurmountable.

Obama has repeatedly sought to tie McCain to Bush’s presidency. When Obama raised the charge early in the debate, McCain quickly responded with the comment that he was not Bush.

Obama shot back that on the economy, McCain was proposing to continue Bush’s policies.

“If I’ve occasionally mistaken your policies for George Bush’s policies, it’s because on the core economic issues that matter to the American people — on tax policy, on energy policy, on spending priorities — you have been a vigorous supporter of President Bush,” he said.

At one point McCain told Obama: “You didn’t tell the American people the truth.” His allegation involved the Illinois senator’s decision to forgo public financing for his campaign in favor of raising his own funds. As a result, Obama has been able to raise much more money than McCain, although the difference has been somewhat neutralized by an advantage the Republican National Committee holds over the Democratic Party.

“He signed a piece of paper” earlier in the campaign pledging to accept federal financing, McCain said. He added that Obama’s campaign has spent more money than any since Watergate, a reference to President Nixon’s 1972 re-election bid, a campaign that later became synonymous with scandal.

Obama made no immediate response to McCain’s assertion about having signed a pledge to accept federal campaign funds.

The first two debates lacked fireworks, but were seen as helping Obama. He appeared poised and knowledgeable — traits that could help undecided voters envision him as president. McCain committed no major errors, but his tone was harsher. He avoided looking at Obama in the first debate, and dismissively referred to him as “that one” in the second.

McCain was more animated on Wednesday. When Obama talked, McCain sometimes took deep breaths, raised his eyebrows, grinned or interrupted his rival.

He accused Obama of waging class warfare by advocating tax increases designed to “spread the wealth around.” Obama denied it, and countered that he favors tax reductions for 95 percent of all Americans while raising them for the richest Americans, those making more than $250,000 a year.

McCain also said Obama has aligned himself with “the extreme aspect of the pro-abortion movement in America” because, while in the Illinois Legislature, he failed to support a measure to ban one type of procedure late in a woman’s pregnancy.

Obama said he supports a ban on late-term abortions, as long as there is an exception for the mother’s health and life. The legislation did not contain that exception,” he added.

McCain sarcastically paid tribute to “the eloquence of Senator Obama. He’s (for) health for the mother. You know, that’s been stretched by the pro-abortion movement in America to mean almost anything.”

McCain repeatedly talked about “Joe the plumber” — an Ohio plumber named Joe Wurzelbacher who on Sunday had complained to Obama about his tax plan, saying it would keep him from buying the small business that employs him.

Wurzelbacher watched Wednesday night’s debate and said he still thinks Obama’s plan would keep him from buying the small business that employs him.

About McCain: “He’s got it right as far as I go.”

Even so, Wurzelbacher declined to say who was getting his vote.