There's an essential paradox about successful women in politics that we flat-footed men have never really grasped.

To succeed in anything, but especially in the cold brutality of politics, you have to be hard as nails, ruthless, willing to win at all costs. Life and love have taught us that these are qualities we associate mostly with the selfish, hardened, ambitious male.

But the few women who do possess these traits are unusually blessed. They are after all, still female, and as such have, or at least are deemed to have also those feminine qualities that speak to a different kind of leadership - maternal solicitude, selflessness, enduring loyalty.

I pondered this chromosomal dimension to political competition as I watched the latest American presidential debate.

The campaign for the Democratic nomination entered a new phase this week. Lagging Hillary Clinton ever farther in the opinion polls with only two months until the first votes are cast, her increasingly desperate rivals have decided to go on the attack.

Instead of politely setting out an alternative that nobody seems to want, they have chosen to come at her with pitchforks and steak knives. At the debate in Philadelphia on Tuesday night, they went for the jugular and it wasn't an edifying spectacle.

There stood Mrs Clinton, the little woman, caught like a frightened doe between her two principal rivals. The shameless John Edwards pounded her repeatedly over her tough foreign policy stance and her dishonesty. Barack Obama, the more reluctant pugilist, landed softer jabs, still designed to tenderise her. From the wings, the also-rans - all male - threw a few lusty punches.

Needless to say, the Clinton campaign seized on the opportunity that the spectacle presented. They issued a video after the debate that emphasised the narrative - Little Woman Waylaid by Big Bullies.

It was pure Clinton. Having spent a lifetime insisting that women should be treated exactly the same as men, Mrs Clinton has been quite brilliant at exploiting her femininity.

She campaigned for years for the rights of women to stand up to abusive men, and then defended her husband as he treated vulnerable female employees as playthings for his own sexual gratification. Better still, she exploited her own status as the helpless, wronged wife of a multiple philanderer to launch her campaign for the Senate from the humiliating ashes of the Monica Lewinsky affair.

In that campaign, the most telling moment came in a debate with her Republican rival, Rick Lazio. The witless Mr Lazio had happened upon a brilliant wheeze to challenge Mrs Clinton directly over some issue by striding towards her podium and insisting that she sign some piece of paper. As Mrs Clinton visibly flinched, the election was clinched. Who wants to vote for a man who would treat a woman like that?

Now she's under attack from a whole gang of men, and tactically speaking it's a no-lose situation for her. If her opponents play tough, she can shrink and look like the intimidated woman beset by brutal men. If they treat her with kid gloves - all gallant forbearance and courtly deference - she can open up a can of whoop-ass on them as eagerly as a dockside bully.

Mrs Clinton, of course, is not the first woman to spot the possibilities of this duality. Elizabeth I, when she wasn't putting Spaniards to the sword overseas or lopping off the heads of Catholics at home, softly reminded her courtiers that she had the body of a weak and feeble woman. Margaret Thatcher could beguile any opponent with her feminine wiles even as she demonstrated repeatedly that she was the proud owner of the largest pair of steel balls in the Cabinet.

All this merely emphasises again that her rivals cannot really defeat her. Only Mrs Clinton can. And it is also why the most revealing moment of the debate was a self-inflicted wound.

Asked whether she stood by an earlier remark that she supported a plan by the Governor of New York to give driving licences to illegal immigrants, she said, essentially, of course she did. But when one of her opponents said he didn't agree - that driving licences were a privilege that ought not to be extended to people who were here illegally, Mrs Clinton backtracked furiously.

It was a startling moment - a rare blunder and an insight into the candidate's fundamental weakness - a powerful impression that she will say and do anything to get elected, even if it means contradicting herself in consecutive sentences. It was a reminder, too, that for all the advantages she and the Democrats possess, both remain deeply vulnerable.

It's been tempting to write off the Republicans, but history suggests that it would be unwise. They have proved remarkably good at winning elections. Since the Republican party was founded in the middle of the 19th century there have been 39 presidential elections. In 23 of those the winning candidate secured a majority of the popular vote. Of those majority winners, 17 were Republicans – beginning with Abraham Lincoln in 1864 and ending with George Bush in 2004 (there's a pair of bookends for you). Only six of those elections were won by Democrats and, get this, four of those winners were Franklin Delano Roosevelt.

So in 150 years, only three Democrats have been elected to the presidency with the support of a majority of voters — FDR, Lyndon Johnson (by a landslide in 1964) and Jimmy Carter (he scraped home with 50.1 per cent in 1976). Now, to be fair, there have been sometimes been special circumstances - Bill Clinton surely would have won a majority in 1996 had it not been for the late entry of the quixotic Ross Perot as a third-party candidate.

But the numbers are so stark that they suggest something quite enduring. The Republicans have been brilliant at assembling winning coalitions over the years — social conservatives, business interests, libertarians, national security hawks. And it is still true that Americans are, deep down, rather conservative.

For most of the past 150 years the Republican message of free markets, traditional values and a strong defence has seen off a steady succession of ambitious Democratic men. Who's to say it won't do the same for a Democratic woman?

Times Recommends

• Fragility always gets my sympathy vote
• Double it and you get the real jobless total
• Has al-Megrahi paid his council tax?