It was about 20 minutes into the presidential debate when Hillary Clinton was asked the series of questions that made the women watching in Melody Drnach's apartment sit up straighter on the cream-coloured sofa, set down their wine glasses and call for the volume on the TV set to be turned up.

The first televised debates of the 2008 election had been polite and relatively bloodless, but this bout could have gone in almost any direction. The questions to the Democratic hopefuls came from members of the public, who had posted videos on YouTube, and were a welcome break from the bland caution of television professionals. Among the videos selected for broadcast, a cancer sufferer pulled a wig off her bald head, and a man from a long line of soldiers displayed the flag that had covered the coffin of his eldest son, who had been killed in Iraq.

But the women gathered in Drnach's apartment in Washington that July evening this year were still taken aback at the line of inquiry directed at Clinton. There was something novel about a candidate for the US presidency being asked: Are you woman enough to be in the White House? And, if you do get elected, how can we be sure you would do a better job for women than any of the male candidates? How would you negotiate with leaders of Muslim states where women do not enjoy equal rights? Clinton didn't miss a beat. "There isn't much doubt in anyone's mind that I can be taken seriously," she said.

Drnach, who was wearing a Make History T-shirt from the Clinton campaign, was so excited she jumped out of her seat. "That's what having a woman in the race does! Can you imagine? Iit's terrific that they are up there arguing about who is going to be a better president for women."

The singularity of Clinton's candidacy was not always expressed in ways that Drnach would have liked. The most talked-about news story that day was a fashion item in the Washington Post deconstructing Clinton's neckline. Did the sliver of flesh above her V-neck top really constitute cleavage; and if so, what was its message? But serious questions were being asked as well. Why had it taken so long for a woman to have a serious chance of becoming president? How would women and men respond to Clinton's candidacy? If Americans did elect a woman in 2008, how would Clinton be any different from the 43 men who had occupied the White House before her?

Clinton was clearly a hit among Drnach's mainly young, single, professional and white guests. "It's mostly the gender," admitted one of them, Jill Cartwright, a law student. "Just as a woman, I feel that a woman can represent my interests better - no matter how liberal or progressive a man is."

But the journalist and women's rights activist Gloria Steinem says support for Clinton generally breaks along class lines. "They say you can tell a Hillary supporter by her shoes. If she is wearing nurse's shoes, or waitress's shoes, she supports Hillary," Steinem told me. "Overwhelmingly, women of colour, single women, poor women who have a better sense of their interest in issues, are for Hillary." In a series of focus groups conducted by the Centre for the Advancement of Women (CFAW), the former first lady was consistently among the women they most admired. Among Latina women in Los Angeles, she ranked ahead of Mother Teresa. African-American women in Philadelphia put her just behind Oprah Winfrey and the R&B singer Fantasia. White women in Memphis also gave high ratings to Clinton, along with Winfrey and a television evangelical. There was respect in all three cities for her intellect, and her apparent calm when forced to deal with her husband's infidelities. "The whole world knew, and she handled it just perfect," one of the Latina women in LA said approvingly.

Like Drnach's guests, these women were motivated by the idea of any woman running - and of attaining the power to make a difference to their lives by improving working conditions, childcare and healthcare, as well as introducing more liberal policies on abortion. "Whether she was conservative or liberal or whatever, the fact that we had a woman president would start to help us," said one woman in Memphis. Although Clinton had voted in favour of the invasion of Iraq, and been slower than many politicians to qualify her support for the occupation, the women believed that a female president would not rush to war. "I hope that she would think twice," said one Latina woman in LA. "She would think as a mother: how would this affect my children, how would this affect my family?"

America had been shuffling through images of Clinton for 15 years by the time she declared her candidacy for the Democratic nomination in January this year. Career woman, doting mother, man-hating radical feminist, saviour of the world's downtrodden, backroom strategist, political helpmate and first lady, betrayed wife and senator from New York: Clinton had either played those parts or been assigned them by her opponents. Now she had embarked on her most ambitious transformation yet.

Perched among embroidered throw cushions and silver-framed family photographs in the sunroom of her Georgetown mansion, Clinton announced she was running for president. But it was not just a declaration of a campaign; Clinton had constructed yet another persona. She was the first woman presidential candidate to have a powerful political machine behind her. Nobody else could claim to have had as close a view of the workings of the White House. In her eight years as first lady, she developed relationships with world leaders that no other candidate could match. And no other candidate could claim to have ready access to the contacts book of that natural-born schmoozer, Bill Clinton. It was an incarnation that demanded to be taken seriously. "I'm in. And I'm in to win," she said.

Even Clinton's enemies conceded that the senator for New York state was not just the best-prepared Democrat candidate, but the strongest of any party. This was not an unqualified blessing: to some, the thought of Hillary Clinton in the White House was not so much a first for women as a second turn for the Clintons. Amid a field of candidates who could also claim to be potential history-makers - Barack Obama as the first African-American and Bill Richardson as the first Latino on the Democrats side, and Mitt Romney as the first Mormon for Republicans - voters were asked whether they would really be striking a blow for progress by backing Clinton. A homage to George Orwell's 1984 surfaced on YouTube, showing rows of blank-faced automata listening to the droning voice of Hillary Clinton, the authoritarian Big Sister. The message was clear: a vote for Clinton was a vote for the status quo.

Unless, of course, you were a politically engaged woman in need of encouragement. It is just 29 years since the first woman was elected to the Senate in her own right, rather than appointed to replace an inconveniently deceased husband or father. According to the Inter-Parliamentary Union, the United States ranks 67th - between Zimbabwe and Turkmenistan - in terms of the representation of women. That translates into 16% of the seats in Congress: 71 women members in the 435-seat House of Representatives, and 16 in the 100-seat Senate.

The closest any woman so far has come to supreme power was Geraldine Ferraro, who ran for vice-president alongside Walter Mondale on the Democratic ticket in 1984. The pair lost heavily to Ronald Reagan and George Bush Sr, but not before a columnist in the Denver Post had sneered about what might happen should Ferraro somehow become president. "What if she is supposed to push the button to fire the missiles and she can't because she has just done her nails?"

Until Hillary Clinton, no woman had ever been a viable candidate for president. "There is no question in my mind that gender was - and remains - a huge factor," says Carol Moseley Braun, whose attempt to become the Democratic candidate in 2004 collapsed before the first votes were cast. "My campaign was almost entirely inspired by my then 10-year-old niece, who was looking at her social studies books and saying: 'But Auntie Carol, all the presidents are boys.'"

A Clinton victory is by no means a foregone conclusion, however. A few weeks into the campaign, the independent Pew Research Centre for People and the Press polled the public for their first impressions of the would-be presidents. The words that came to mind when people thought of Hillary Clinton were: Bill, husband, intelligence and strength, but also phoney, sneaky, way too feminist, backstabber and she-devil. Even among the CFAW's focus groups, some of the members openly hated Clinton. "I think she's a pig. I think she's a liar. I think she's a cheater. I think she is insincere," said an African-American woman in Philadelphia.

Clinton's apparent abandonment of liberal ideals - such as her search for common ground with the anti-abortion lobby - has also made her suspect on the left. The actor Susan Sarandon, a prominent supporter of liberal causes, was scathing. "I think she's a politician like everyone else," she told the British journalist Jonathan Dimbleby last year. "I'd like to find somebody that really has a moral bottom line, be they man or woman."

The odds are, Clinton will hear much worse in the coming months. As any woman running for office knows, it is open season on her husband, her children, even her hair and her clothes. The harshest critics are often other women. Pat Schroeder, a left-leaning member of the House of Representatives from Colorado, had a brief run for the presidency in 1987, but with seven Democrats already in the race, soon concluded that she could never raise enough funds. Before she pulled out, she had women mailing her style tips - and cheques so she could get her hair done. A few years earlier, Ferraro had encountered outrage among some women that she had dared to play in a male arena. "They figured that if I were doing a man's job - the second most important job in the world as vice-president of the United States - their husbands would look at them and say, 'What are you doing?' and they would suffer by the comparison," she told me.

For many women - even fellow Democrats - Clinton's journey from presidential wife to presidential candidate is a source of disquiet. "I find it deeply annoying when people make her into some kind of feminist heroine," complains a lawyer from Cincinnati, Ohio, who like Clinton is entering her 60s. "This is a woman who is where she is because of who she married. I don't think she would ever have got there if she hadn't been married to him, and stuck with him, and that's fine. But that's not the feminist message you want your daughters to receive, is it?"

The Christian right and anti-feminists, meanwhile, see in Hillary Clinton a symbol of all the negative changes America has undergone over the past 40 years, and the remaking of the roles of wife and mother, husband and father. When Clinton was endorsed by the National Organisation for Women, a Christian women's group known as the Concerned Women of America put out a sour statement asserting: "Hillary needs a reality check if she thinks that a majority of women voters embrace radical feminism."

It would be impossible for any candidate to satisfy all these constituencies, claims Marie Wilson, the director of the White House Project, which trains women for leadership. Wilson argues that the intense and competing views of Clinton have less to do with her personality and policies than with women wielding power. "We are still fighting against things that are deep in the culture, and she is the place where we have that conversation," says Wilson. "We don't say we are concerned about ambitious women; we talk about Hillary Clinton. Because she is the first, she has tested many of the issues that are really not about her, but about the deeply cultural issues that have kept women out of leadership."

When it comes down to it, did Braun, Ferraro and the other women fail simply because the public won't elect a woman? Opinion polls suggest more than 90% of Americans would be ready to vote for a woman president. More than half believe America would be better off if it were led by a woman. But ask the same person if they think the average American is prepared to accept a woman as president, and the answer is rather different. Only 55% of those polled say the country is ready, and among women the figure is just 51%.

The different figures are reminiscent of polling on African-American candidates, where there is often a wide gap between the number who say they would vote for a black person, and those who say their friends and relatives would not. What it suggests is that there are plenty of reasons that the country is not ready to vote for a woman - even if people are not prepared to say them out loud.

No jacket, no tie ... But what would a female president look like?

Pat Schroeder, who briefly ran for the Democratic nomination 20 years ago, believes Americans simply cannot conceive of what a woman president would look like. "It is still really hard for women to have that working image that men have," she explains. "We know what they do. They loosen their tie and collar, and throw their jacket over their shoulder. They talk on a cellphone. If they want to look tough, they play touch football." Women, Schroeder says, don't have a "uniform" for politics, unlike men with their "red tie, white shirt, blue jacket".

"The script hasn't been written yet," agrees Carole Moseley Braun, who ran for the Democratic candidacy in 2004. "The visuals don't exist for a woman in leadership." Perching on a stool during a debate might allow male candidates to look casual and relaxed, she says; for women, it is a nightmare of worrying whether their slip is showing.

American voters have become accustomed to seeing pictures of would-be presidents engaged in an array of manly leisure activities, all designed to demonstrate that at heart they are just ordinary folk. It's unlikely that they will ever see a photograph of Hillary Clinton throwing a football, or shooting ducks. They definitely won't see her windsurfing, or doing anything that involves a swimming costume - not after paparazzi captured her from the rear on a beach in 1998. Clinton's favourite outdoor pursuit is walking, and when she wants to de-stress she cleans out her closets - neither of which are particularly photogenic.

Film and TV don't help. Cinematic representations of a woman in the West Wing are exceedingly rare and seldom heroic. In the 1964 film Kisses for My President, the improbably elected female leader of the free world resigns when she gets pregnant. Her husband rejoices that while it took the votes of millions of women to put the president in office, it took only one man to get her out.

Television recently proved more PC with Commander-in-Chief, although the show only lasted one season and even it couldn't stretch to showing a woman beating a man in a presidential election. The main character, Mackenzie Allen, is a vice-president who takes over from her boss after he dies in office. She does so only after ignoring demands from political opponents and members of her own party that she step aside for someone more appropriate - in other words, a man.

Suzanne Goldenberg