By John Whitesides, Political Correspondent

HEMPSTEAD, New York (Reuters) - Republican John McCain and Democrat Barack Obama face off in their final debate on Wednesday, with McCain needing a strong performance to begin to turn around a White House race that could be slipping away.

Three weeks before the November 4 election, McCain is running out of chances to reverse his slide in national opinion polls and gain ground on a surging Obama.

The 9 p.m. EDT (0100 GMT Thursday) encounter at Hofstra University in Hempstead, New York, will be the third and last debate between the presidential contenders and their final opportunity to reach a television audience of 60 million or more.

"You can do yourself a lot of good when you have a debate with that many people watching," South Carolina Republican Party Chairman Katon Dawson said.

The debate comes as opinion polls show Obama gaining strength nationally and in battleground states after weeks of economic turmoil and plunging stock markets, with more voters saying they trust Obama's leadership on the economy.

A Reuters/C-SPAN/Zogby poll gave Obama a 4-point edge over McCain, but other national polls showed a larger margin for the Illinois senator. A CBS News/New York Times poll showed Obama leading by 14 percentage points, the fifth survey this week to register Obama's lead in double-digits.

The bad poll news heightened the debate stakes for McCain, who unveiled a package of measures on Tuesday to help investors, particularly older Americans who have seen their retirement savings decimated by stock market losses.

The Obama campaign was eager to raise the stakes for McCain.

"It's his last chance to somehow convince the American people that his erratic response to this economic crisis doesn't disqualify him from being president," Obama spokesman Bill Burton said in a memo to reporters.

McCain has indicated he is likely to bring up Obama's relationship with former 1960s radical William Ayers. The two served on a community board in Chicago together and Ayers hosted a political event for Obama early in his career.

Obama had noted McCain's reluctance to discuss the issue with him directly during their last encounter.

"DIDN'T HAVE THE GUTS"

"I was astonished to hear him say that he was surprised that I didn't have the guts to do that," McCain said in an interview with KMOX radio in St. Louis, Missouri. "I think he's probably assured that it's going to come up this time."

Several recent polls have shown McCain's attacks on Obama's character have largely backfired, increasing unfavorable opinions about McCain among voters looking for solutions on the economy.

"There is no question the negative campaigning just isn't working," pollster John Zogby said. "To make an impact in this debate, McCain needs to be proactive and be very specific about the way he would lead an economic recovery."

McCain adviser Nicolle Wallace said on CBS's "Early Show" the Arizona senator would focus on explaining how he would be the best leader to heal the financial chaos of the last month.

"We are in a major national crisis. And in an hour of crisis, John McCain is someone who has actually reached across the aisle, worked with Democrats to take on big, entrenched special interests, and has a record of reform," she said.

Before heading to New York, Obama shook hands with several dozen supporters outside the Ohio resort on the banks of Lake Erie, where he has spent the last three nights in debate preparation.

"We want to call you Mr. President," shouted one woman.

"I've got a little more work to do," Obama replied.

The presidential debate will focus on domestic policy and the economy. Obama and McCain will be seated at a table with moderator Bob Schieffer of CBS News instead of standing at podiums as in the first debate.

That could provoke more direct exchanges than in the first two encounters, which did little to recast the presidential race. While Obama just needs to avoid any major mistakes, McCain needs a sharper performance to build momentum for the final 2 1/2 weeks on the campaign trail.

"He has time to come back in this race," Dawson said of McCain. "Every day is a lifetime in American politics. But he has to get started."

(Additional reporting by Arshad Mohammed and Matt Spetalnick; Editing by Doina Chiacu)