This display of hypermasculinity in the midst of wartime, some concluded, would have a particular appeal for women voters. Republican speechwriter Peggy Noonan said that she half expected Bush to "tear open his shirt and reveal the big S on his chest". One Wall Street Journal columnist pronounced him "a hottie". Rightwing talkshow host G Gordon Liddy proclaimed that the president "has just won every woman's vote in the United States of America".

Paradoxically, it seems that the women he appealed to most are those who are already hitched. The women most likely to be on the lookout for a "hottie", namely single women, are increasingly devoted to his Democratic rival John Kerry.

With six weeks to go before the presidential election, one of the best ways to find out how a woman is likely to vote is to check her ring finger. A recent poll shows Bush ahead of Kerry among married women by 13%, while Kerry has a 25% lead among unmarried women. Indeed, the difference in voting intentions between single and married women - 38% - is far greater than that between men and women, which stands at 5%.

What has been described as the "marriage gap" could prove crucial, particularly for the Democrats. Women settle on their presidential choice later than men, and so comprise most of the small number of coveted undecided voters that remain. In a race this close, the party that can identify the women who are most likely to identify with the party could make the difference between victory and defeat - so much so that pundits have invented a new political construct just for the occasion. After "angry white men" (1994), "soccer moms" (1996), the post 9/11 "security moms" (2002), and the drag-racing-fanatic "NASCAR dads" (2003), there is now the "Sex and the City voter". The term may jar, but the phenomenon could provide a jolt. Single women represent at least 24% of the voting-age population and a massive 46% of voting-age women.

But if the Democrats are going to win, say the pollsters, they are going to have to woo single women relentlessly. To that end, they launched a programme called Take Five last month, which encourages the faithful to convince five single women who don't usually vote to go to the polls.

The marriage gap is not new. But each election year it has grown increasingly huge, more than doubling over the past 20 years. Views differ on why this should be. Some of it can be explained by other demographic factors that are related to, but not defined by, either marital status or gender. According to the census, more than half of unmarried women earn less than $30,000 (£16,800) a year, while more than half of married women have annual household incomes of more than $50,000 (£28,000). And the wealthier you are, the greater the likelihood that you will vote Republican.

Personal factors also play a role. Married women often vote the way their husband does. "I registered Republican when I got married," Ginny Savopoulos told USA Today. "But after I was divorced I was thinking more about, what's out there for me as a single woman?" After struggling to find work as a paralegal, she was laid off two years ago and remains disenchanted with the war in Iraq. Still registered as a Republican, she plans to vote Democrat.

The experience of having children further deepens the divide. Married women with children are even more heavily Republican than those without, while childless single women are even more sympathetic to the Democrats than unmarried mothers. Of the 10 states with the highest birthrates, all but one voted for Bush in 2000. "Conservative, religious-minded Americans are putting far more of their genes into the future than their liberal and secular counterparts," wrote Phillip Longman, a senior fellow at the New America Foundation, in a recent article for the Washington Post. "If Metros don't start having more children, America's future is Retro."

But policy issues related to the current political climate also play a role. Married women place a higher priority on the war on terror and are more likely to value Bush's leadership, while single women are more concerned with such issues as health insurance and policing. "It's not that single women aren't worried about security," says Kellyanne Conway, president of WomenTrend, a woman-centred polling organisation. "But they are more likely to be concerned with job security and whether it's safe to get home than the war on terror.

"They're not so interested in small government because to them, the government is a partner and a safety net. For those women without husbands, Uncle Sam and Big Brother are the greatest protectors."

The Republicans have adapted their message accordingly. As supporters in Madison Square Garden waved signs declaring "W is for Women", Laura Bush's prime-time convention speech was aimed squarely at parents: "I want to talk about the issue that I believe is most important for my own daughters, for all of our families, and for our future," she said. "George's work to protect our country and defeat terror so that all children can grow up in a more peaceful world."

But the Republican approach also repels many singles. "Republicans have this programme of trickle-down dignity," says Bella DePaulo, who studies singles' behaviour at the University of California at Santa Barbara and is currently writing a book called Singled Out. "They portray a woman's life as in a family with mum, dad and the kids and have shut the door on anyone who doesn't fit into that."

Claudia Bernett, a single, 32-year-old digital designer in New York, plans to vote against Bush. "I'm not a great fan of Kerry but the Democrats at least say their intentions are to generally take care of people, while the Republicans are so brutal. Abortion is crucially important, but there are other agendas that even exceed that one - we seem to be at a very dangerous moment in time." Such views should present an opportunity and a challenge to the Democrats. The main reason the gender gap opened up in the first place, in the 80s, was not because they were doing so well among women but because they were losing so much support among white men, just over a third of whom backed Al Gore at the last election.

For while single women are currently much more likely to vote Democrat, they are much less likely to vote at all. In 2000, Gore won the single women's vote by 31%, while Bush had just a 1% lead over married women. The trouble is, that while 62% of married women voted, only 43% of singles did.

"If unmarried women in Florida had turned out in the same percentage as married women, Al Gore would have won the state easily," Democrat pollster Celinda Lake said earlier this year. Indeed, if they had turned out at just the statewide average, then Gore would have won by a relatively comfortable 63,000.

So why didn't they? Because nobody asks, says DePaulo. "Just listen to the rhetoric of the politicians," she says. "It's so much family values - it's as though single people don't exist."

But the Democrats have been slow to grasp the existence, let alone the potential, of this enormous untapped resource. During the Democratic convention Kerry did not emphasise issues such as the economy or health care, which would have appealed to undecided women voters, but instead tried to outmacho Bush with his war record. Since this backfired he has returned to the kind of domestic issues that could well galvanise single women into making up their minds - not between Kerry and Bush, but between Kerry and not bothering. Whether he succeeds or not will largely depend on whether he has anything more to offer them than the chance to put two more men in the White House.

"The trouble with going after single women, those fans of progressive change, is that one has to offer them something progressive," wrote Katha Pollitt, a columnist for the leftwing magazine the Nation.

"It will be interesting to see if the Democratic campaign to sign up these voters involves offering them things they want."