Sour grapes? Maybe. After all, Ms Myers was an indifferent presidential press secretary, remarkable only for having been the first woman to hold that post. Forced out at the end of 1994, she has resurrected herself in the same way as many American public figures who have fallen on hard times - as a TV talk-show host. But for Bill Clinton, her charges cut to the quick.
From the very moment he was elected, this President has cultivated the female vote. As he named his Cabinet, he promised an administration that "looks like America", featuring women and minorities as none before it. And he delivered - though not without denouncing as "bean-counters" certain women's groups who complained he was still not doing enough. Today, the White House operates a busy "women's outreach section". Legislation, speeches and public appearances are all crafted to appeal to women. The strategy is paying off. Among women Clinton leads Bob Dole, his likely opponent in November, by an astounding 27 points (62 to 35 per cent), according to one recent new poll - four times his lead among male voters. But Ms Myers raises the eternal question about Bill Clinton: does he really mean what he says?
This President's contrasts are an armchair psychiatrist's heaven. In his attitude to women, as so much else, two competing and utterly different personas jostle. One is the lifelong political progressive, the Yale alumnus and Rhodes scholar who is genuinely outraged by unfair barriers to women's advancement. But then there is the other Bill Clinton, the Southern bubba whose private life (at least as recounted by the likes of Gennifer Flowers and Paula Jones) bespeaks a view that women are sex objects to be plucked from the secretarial pool. One President Clinton loves to convene White House events called "Working Women Count", declaring that "from the first day I met Hillary, it never occurred to me we wouldn't have a two-worker home". Having uttered such stirring words, the other President Clinton loves to round up his chums and indulge in all-male group therapy on the golf-course. Brains and bimbos - in the Clinton universe the twain rarely overlap.
Which leads, of course to his wife, the brainiest non-bimbo of them all. In the first two years of the Clinton White House, any suggestion that women were subtly kept out of the inner circles crumbled before the unassailable fact that the President's closest, most influential adviser was Hillary. Did not male staffers walk in dread of her - did not minions take a raising of her eyebrow as an order to sack the entire White House travel office? And Hillary was running healthcare reform, the biggest single item on the Clinton legislative agenda. Who could possibly argue that women were on the sidelines?
But Hillary Clinton's star has faded. Health reform collapsed ignominiously in September 1994. She, far more than her husband, is demonised as a big government liberal; she plainly is a more central figure in Whitewater (assuming, of course, that Whitewater has a centre). In the polls, her approval ratings have slumped to a point where the First Lady has turned into First Liability. Ms Clinton may remain a power behind the throne, but no longer does she act like one. At which point, critics say, Bill Clinton's women's policy is exposed for the charade it is: a hypocritical contrivance to impress a voting group crucial to his re-election hopes, a Potemkin village of female faces masking the reality of a good ol' white boys club.
But that view is as much a caricature as the one it is trying to debunk. The Clinton White House is certainly male-dominated. Its most powerful figures are Leon Panetta, the chief of staff and his deputy Harold Ickes, advisers such as George Stephanopoulos and Bruce Lindsey who worked on the 1992 campaign, and the President's boyhood friend Thomas "Mack" McLarty, and Mike McCurry, the press secretary.
It was Mr Panetta who engineered the McCurry succession last year, shortly after he had been installed by Mr Clinton to knock order into a chaotic White House operation. The brutal tactics he employed to force out Ms Myers made him the feminists' arch-villain, a man who in matters of working women "just doesn't get it". And Ms Myers was but one of several middle- ranking women to leave around the same time, among them Mr Clinton's Cabinet Secretary, Christine Varney, and Joan Baggett, director of political affairs. The White House was a shambles, many women there acknowledged - but why should they alone pay, not some of the men who had also manifestly failed?
The truth, however, is more complicated. Ms Myers claims, and justly, that she was denied the access and information to perform her duties. But however likeable, she simply did not measure up. Mr McCurry's easy authority is no small reason for Mr Clinton's improved fortunes. Rather the tale of Ms Myers, why she was given the job and how she lost it - after a tearful Oval office meeting with the President in which defeat was dressed up as victory - speaks volumes for Mr Clinton's slippery modus operandi and his ambivalent attitude towards the other sex.
Still, women are more in evidence than in any previous White House, even if they haven't yet been promoted to the praetorian guard. Mr Clinton's chief domestic policy adviser, his new Cabinet Secretary, his Director of Intergovernmental Affairs, and his Director of Public Liaison are all women - as are Nancy Soderberg, staff director at the National Security Council and architect of Mr Clinton's Irish policy, and Laura Tyson, head of the National Economic Council and the President's senior in-house economic adviser. True, former Budget Director Alice Rivlin has just left, but for the at least equal post of vice-chairman of the Federal Reserve.
"Maybe a sort of glass ceiling does exist at the White House," says Anita Perez Ferguson, President of the National Women's Political Caucus, "but before now, every one of those jobs would have been filled by a man. And look at the rest of the administration: it has record numbers of women, at much higher levels than before." Indeed, 40 per cent of all Mr Clinton's higher echelon appointments have been women, twice as many as under George Bush and four times the number in the Reagan administration. "And this is not just at `soft' agencies, like Health or Education, where women have always been well represented," Ms Ferguson stresses, "but across the board."
Take the Cabinet-level appointments. For three years now, Janet Reno has served as the first female Attorney-General in US history, the first woman to hold one of the "big four" cabinet posts of State, Defence, Treasury and Justice. Ah yes, contend her critics with some reason, but Ms Reno is merely a figurehead. Then, however, those same critics point to the true power at the Justice Department - another woman, in the person of Jamie Gorelick, the Deputy Attorney-General. The extravagant travel schedule of Hazel O'Leary, the Energy Secretary, has been widely noted, but so, too, has her admirable exposure of the shameful truth about radiation experiments performed on unknowing US citizens in the early nuclear era. True, Donna Shalala, the Health Secretary, was virtually frozen out of healthcare reform. But who was in charge? Not some male golfing partner of the President, but another woman, Hillary Clinton.
Then there is Madeleine Albright, a highly visible and effective UN Ambassador who has actually won some policy arguments with the white boys. Now she is a prime contender to replace Warren Christopher as Secretary of State if Mr Clinton wins a second term. And only last week a sixth woman achieved Cabinet rank, when Charlene Barshefsky was named the new US Trade Representative, a post that in this age, when global rivalries are economic as well as military, in some respects matters almost as much as Secretary of State.
On other fronts, too, the feminist cause has advanced. Mr Clinton chose a second woman, Ruth Bader Ginsburg, to sit on the nine-member Supreme Court. For the first time a woman holds one of the top three jobs at the CIA. Not quite a Stella Rimington sensation, to be sure, but positively revolutionary for the CIA, one of Washington's great bastions of male chauvinism. One way and another, the bean-counters haven't done too badly.
And even if Bob Dole wins, all will not be lost. A crusty 72-year-old white male from Kansas may seem an unlikely trail-blazer in gender politics, but Hillary Clinton might pale beside First Lady Elizabeth Dole, a political operator to her fingertips and - as the only woman ever to have held Cabinet jobs in two different administrations - a veritable pulveriser of glass ceilings. Then there is Sheila Burke, Mr Dole's chief of staff. A Republican victory would put her in line to become the first female White House Chief of Staff, a post whose power is exceeded only by that of the Presidency itself.
Even if Clinton loses, therefore, significant advances may be in store for the monstrous regiment. So why do women voters not warm to Mr Dole? The answer reaches beyond his stiff and stern demeanour. Unlike countries as disparate as Britain, India, Pakistan, Canada, Turkey, Israel and Norway, the US has never had a female head of Government, nor does it look like having one any time soon. But at least Bill Clinton has raised the glass ceiling a little closer to that unattainable summit.