WASHINGTON - President Barack Obama and Mitt Romney face off in their third and final prime time debate on Monday in the critical swing state of Florida as each man looks for the knockout punch that could break their dead heat in the polls with just two weeks until election day.

On the eve of their foreign policy debate in Boca Raton, Florida, a new NBC News/Wall Street Journal survey showed the men are tied at 47 per cent. The president has a wider lead among all registered voters - 49 per cent compared to 44 per cent for Romney - but the new poll suggested his support has weakened among women, a key demographic for Obama in his bruising battle for a second term.

The president’s lead among female voters has slipped to its slimmest margin this year - 51 to 42 - in the NBC/Wall Street Journal poll. Romney, meantime, still has a 53 per cent advantage among men compared to 43 per cent for Obama.

On Monday, the debate is about how America deals with the world - and how it should.

If the moderator, Bob Schieffer of CBS News, has his way, it will be the most substantive of the debates. He has outlined several topics: America’s role in the world, the continuing war in Afghanistan, managing the nuclear crisis with Iran and the resultant tensions with Israel, and how to deal with rise of China.

The most time, Schieffer has said, will be spent on the Arab uprisings, their aftermath and how the terrorist threat has changed since the attacks on Sept. 11, 2001. No doubt the two candidates will spar again, as they did in the second debate, about whether the Obama administration was ready for the attack in Benghazi, Libya, that killed Christopher Stevens, the American ambassador, and three other Americans. Romney was widely judged to not have had his most effective critique ready, and this time, presumably, he will be out to correct that.

The early line is that this is an opportunity for Obama to shine, and to repair the damage from the first debate. (He was already telling jokes the other night, at a dinner in New York, about his frequent mention of Osama bin Laden’s demise. Nonetheless, Romney has to start making big gains in several battleground states - Florida, Ohio and Virginia, especially - if he’s to wrest the White House away from Obama. Those states will determine the outcome of the Nov. 6 vote. Polls in several of the battlegrounds have also tightened, though Obama still maintains an edge. Both politicians have been barnstorming key swing states in recent days and will continue to do so in the final stretch of the campaign.

Republicans say the polls prove Romney is riding a wave of momentum.

“I like what I see, because the trend is in our direction,” Ohio Senator Rob Portman, a top surrogate for the Romney campaign, said Sunday. “The enthusiasm and energy are on our side.”

Team Obama, meantime, put on a brave face, shrugging off the numbers by saying they’ve always expected a close race. David Axelrod, an Obama senior adviser, also pointed to state polls, including another NBC /Wall Street Journal survey from late last week that showed the president ahead by eight points in Iowa and six in Wisconsin.

“We feel good about where we are,” Axelrod said Sunday on “Meet The Press.” “We feel we are even or ahead in these battleground states.”

Obama and Romney took a break from swing-state campaigning over the weekend to prepare for their final debate. The 90-minute showdown represents one of the last chances for them to win over the small but critical group of Americans who still haven’t decided how to cast their ballots on Nov. 6.

Obama hunkered down at the presidential retreat of Camp David in Maryland’s lush Catoctin Mountains. Axelrod, White House senior strategist David Plouffe and Tom Donilon, the president’s national security adviser, were with him.

Romney, meantime, spent the weekend in Florida in his own so-called debate camp.

During their second faceoff last week, however, Obama bested Romney on questions about Libya, in particular when the Republican falsely asserted that it took the president 14 days to characterize the attack on the consulate as an act of terror.

The president also disarmed Romney by saying he took ultimate responsibility for what went wrong in the North African country last month.

With those memories still fresh - many commentators called it the worst moment of the debate for Romney - the Republican was expected to try to steer clear of Libya during the Florida showdown, and to instead focus on Obama’s policies on Iran and Israel.

Romney has argued the administration has been soft on Iran as it builds a nuclear programme and accuses Obama of damaging the US-Israeli relationship.

“I think what you’re going to see is Gov. Romney lay out a clear agenda for how to get Iran to do the right thing,” Portman said Sunday.

Axelrod, meantime, backed up Obama’s insistence that harsh economic sanctions against Iran are working.

“They’re feeling the heat, and that’s what the sanctions were meant to do,” said Axelrod, who also ridiculed Romney’s gaffe-ridden foreign trip in July as a “Dukes of Hazzard tour of international destinations.”