Earlier, when your scribe flew into the small airport at Jackson Hole, Vice-President Dick Cheney, who has a house there, had just jetted out on Air Force Two, presumably on the calculation that so small a community could not hold two individuals of such robust conservative views simultaneously.

After the bustle of Minneapolis, where the Republican convention had reached its climacteric, this rural retreat in the Rockies was a refreshing change. Wyoming is hardly a swing state: in 2004 it voted 69% for Dubya, 29% for Kerry. Of its 23 counties, Teton is the only one that narrowly went to Kerry. With an average house price of $1.7m, that is understandable.

It takes a conscious effort to adjust to the contrasting demographics of US politics vis-à-vis British. In this country, a deprived area is assumed to be safe Labour territory; leafy suburbs, momentarily colonised by Tony Blair, have now reverted to probable Tory allegiance. In America, wide lawns with sprinklers, 10-bedroom houses and a driveway full of expensive cars denote the abode of Democrat-voting liberals with social consciences, environmental awareness and a penchant for late term abortions.

Americans enjoy their elections and, contrary to British caricature, are well informed about them. On the wide-screen TV in the bar the NY Giants were doing things to the Washington Redskins that are surely banned by the Geneva Convention, but the election chat would not have disgraced Newsnight. When one looks at the US presidential contest from opposite sides of the Atlantic the view is startlingly different.

Whatever happened to Barack Obama? It seems a century since he stepped out from his Pearl & Dean Corinthian arch to posture in front of a mock-up of the West Wing before the adoring members of his cult. That is Obama's biggest problem now: he is beginning to seem like a memory. His campaign has deteriorated from the slickness of New Labour circa 1995 to the chaos of that camp today, except that Obama's people took just 48 hours to achieve a decline that occupied Labour for a decade.

A triangulation has been created that is potentially fatal for Obama. He obsessively targets Sarah Palin, who should be below his pay grade; John McCain carries on an almost uninterrupted conversation with the US public; and Joe Biden dances around his handbag. Great strategy, huh? The Democrats are honorary Brits in their misunderstanding of the US electorate.

The first 24 hours of the Palinolithic Age in American politics saw a reaction from the Democrats that resembled the scenes of mass suicide among doomsday cults. Obama led from the front, with an insult to small-town America that was broadcast from coast to coast within minutes. The vice-presidential candidate's pregnant teenage daughter was skewered like a voodoo doll by caring liberals. The Obama attack dogs went rabid and by the time they had been put under restraint the damage was done – but not where they intended.

Women voters quickly realised that the Democrats talk a good game about fracturing glass ceilings, when the aim is to promote some uberbitch from the Beltway; but if a normal American woman presumes to step out from behind the white picket fence and seek high office they will beat her up. That realisation translated itself, in the Washington Post/ABC News poll, into a 20-point swing to McCain among white women voters. Nice one, Barack.

Obama, however, had a cunning plan to regain that lost ground, with his "lipstick on a pig" quip, from which many of us adduced he has lost interest in politics and would like to spend some time fishing. Meantime, Biden was provoking an unprecedented attack on himself by the influential American Catholic hierarchy and telling the public that Hillary Clinton would have been a better "V-P pick" than himself. "Biden certainly has a credible viewpoint on this," was the dry response from Ben Porritt, McCain's spokesman.

When Sarah Palin survived a marathon three-hour grilling on ABC by a hostile interviewer asking blatantly trick questions, with only one hiccup (she did better than Dubya in 2000), Democrat hopes were frustrated. Now former Clinton aide Dick Morris is describing Palin as "an authentic model of feminism" and predicting a Palin/Clinton cat-fight for the presidency in 2012, which indicates fairly clearly which team he expects to win this year.

Behind all this wind and fury, with the polls roughly level, lurks the enigmatic figure of the American voter. Only a rash commentator would call this election one way or the other; but if Obama wins it will be in spite of his campaign, not because of it.