Gillard has failed to connect with voters

Ms Gillard has had unpopular predecessors, but none has excited this level of personal vituperation or the obvious resentment of her gender and fundamental dispute of her right or capacity to govern.

Last week alone provided not only a fair average sample of appalling sexism, discourtesy and want of respect for her or her office, but also a practical demonstration of how much of it goes beyond some difference of political leaning, disagreement about policy or preference for someone else to a seemingly intense and bitter hatred of the person herself. It demeans our polity, our times and the public discourse.

Not only does it invite sympathy for what she has to endure but worry that such abuse will deter other women from aspiring to political leadership.

Australia has a tradition of robust political debate, which has included, from both sides, a fair amount of playing the person rather than the ball, but the abuse directed at Ms Gillard is not only well out of court but reaching the point where the disgust and anger aroused by their doing so is plainly counter-productive. It has been so bad there will be some who will say the experience of her three-year term showed Australia was not mature or civilised enough for a female leader, or that the ultimate source of her political failure lay in the incapacity of men in particular to treat her seriously or with respect. Those who say this will have examples enough, many shameful, but they will be talking tosh.

There is a particularly nasty and sexist edge to the abuse of Ms Gillard, but it hardly comes from anything approaching a significant proportion of the population.

Ms Gillard was an able and popular deputy leader before she became Prime Minister, and there is little evidence of any particular animus then being focused at her or her sex. Her taking the leadership was brutal, but that has not deprived other leaders with blood on their hands from developing popularity and respect, understanding of their ruthlessness, and a sense of authority and legitimacy in the electorate.

When Ms Gillard shortly after went to an election, she did not achieve majority government, but she went into negotiation to form minority government with the moral power of a two-party preferred majority. Her opponent may have resented his own failure and embarked on a remarkable display of oppositionism - one bound to come back and haunt him - but she has had a remarkable record of getting her legislative proposals through the parliament.

Though she has been undermined by Kevin Rudd on her own side of politics, she has had no difficulty (until recently at least) in wielding control over the whole party.

What has not happened, however, is some settling of her position in the electorate. She has been consistently unpopular with voters. Attacks alleging her to be a ''liar'' over her change of position on the carbon tax hurt her standing, but primarily because she gave no apology and no explanation, and made little effort even to sell the idea of the need for taxes on carbon pollution.

At the heart of her problem has been a failure by the enormous public relations machinery of her government to take the electorate into her confidence, to explain what she has been doing and why, and to eschew the fakery and spin for frank talk and honest explanation. Her problem is not so much that many people see her as a liar, as that they do not believe her, do not trust her, and feel they cannot discern her amid all of the unconvincing packaging.

Other women in politics face unacceptable extra hurdles because of their gender, but have not faced the problems of Ms Gillard. It would be a pity if she was to use misogyny as her alibi for defeat.