On Wednesday evening, as Sarah Palin was preparing to take the stage at the Republican convention, a knot of teenagers was standing on a footbridge over the highway leading into Minneapolis-St Paul with a homemade sign that read: “Obama ’08”.

Had they nothing better to do? “It’s the first time that I’ve felt like this,” explained Ligeia Baumhofer. “Barack Obama has got us excited about politics.” A policeman told them to move their sign inside the railings and advised them to leave. But they stayed to breathe more traffic fumes and wave at car drivers honking their approval.

There is phenomenal passion being shown by his supporters and, while most polls still point to a tight contest, some evidence suggests that the Republicans are falling into an “enthusiasm gap”. A CBS survey this week suggested that 55 per cent of those backing Mr Obama were feeling more energised — and therefore likely to vote — than usual, compared with 35 per cent for John McCain.

The Republican convention in St Paul began badly. Monday’s proceedings were wiped out by Hurricane Gustav and Tuesday evening’s events drifted from dreary to dull. Joe Lieberman, who eight years ago was the Democratic vice-presidential pick, was almost languid in his defection. When this long-serving Senator calls for Washington to be “shaken up”, it must be because he does not like cocktails stirred.

Indeed, the Xcel Energy Centre in St Paul was not living up to its name. Across the river in Minneapolis, Congressman Ron Paul was holding a rally for 10,000 libertarian-leaning Republicans but inside the convention hall itself there were rows of empty seats. Denver, where Mr Obama had packed 84,000 into a football stadium for his acceptance speech, seemed along way away.

Tirso del Junco, an 83-year-old Cuban exile at his twelfth convention, conceded that the Democrats had “put on a better show”. Walter Hatch, 23, gazed around the emptying party that had been put on for the Florida delegation and said: “The crowd here is mostly old — they probably want to be in bed by 10pm.”

That was before Mrs Palin took the stage to deliver a speech on Wednesday night that set the convention alight. Her imperfections and inexperience, as well as the public spectacle and humiliation being endured by her family, only added fuel to her fire: conservative Republicans love nothing more than rising to defend one of their own against a liberal media.

“I feel like I have been electro-charged,” said Bill Seller, a delegate from Missouri. “She is amazing and it has completely changed our view of McCain. For the first time, I really think they can win this thing.”

Steve Schmidt, Mr McCain’s chief strategist, said: “The race has changed. She has energised and breathed new life into the Republican Party that none of us thought was possible.”

Mrs Palin should ensure that, as in 2000 and 2004, the Religious Right will bang on about abortion or gay marriage, evangelical churches will run buses to the polling places and Talk Radio will roar back on side.

But Mr McCain knows that is no longer enough to defeat Mr Obama on November 4. His campaign manger, Rick Davis, told The Washington Post that the Republican Party’s deep unpopularity after eight years of President Bush means “right now if the election were held today we probably don’t have as many votes as Barack Obama . . .[We] need to not only transcend where our party is but to be able to punch through all these environmental problems.”

So it was that in his own speech on Thursday night, Mr McCain offered much thinner fare to delegates who had feasted on the raw red meat served by Mrs Palin at the convention 24 hours before.

He sometimes subdued his audience in the convention hall by addressing those watching on TV outside. “I don’t work for a party. I don’t work for a special interest. I don’t work for myself. I work for you. Instead of rejecting good ideas because we didn’t think of them first, let’s use the best ideas from both sides. Instead of fighting over who gets the credit, let’s try sharing it. This amazing country can do anything we put our minds to.”

He made only an oblique reference to social conservative issues such as abortion, talking of his belief in “faith, service, a culture of life” as he pitched himself to the disaffected Democrats and Independents more worried about petrol prices, jobs, schools, taxes and foreign policy.

He even had nice words for Mr Obama, the target of Mrs Palin’s sharpest arrows on Wednesday, saying “much more unites us than divides us” and that the Democrat had “my respect and admiration”.

The big difference was that he had the “record and scars” of a lifetime’s service to prove his readiness to reach out across the political divide, while “Senator Obama does not”. But it was a clunky and contorted speech. Here was Mr McCain arguing that he was more experienced and ready to heal “partisan rancour” — when he had, by necessity, chosen a stridently right-wing running-mate with only 18 months in state-wide office.

And he had to work hard to marry what remains of his own maverick appeal after spending 26 years on Capitol Hill (and the past four loyally backing Mr Bush) to that of Mrs Palin, who is so fresh she risks being seen as green. “I can’t wait until I introduce her to Washington,” he said, “change is coming”.

Mr McCain’s strategists insist that Mrs Palin has an “Everywoman appeal”, a “hockey mom” who cooks, shoots, drives herself to work, cares for five children and oh yes, just happens to be running for Vice-President as well. “From the inside, no family ever seems typical. That’s how it is with us. Our family has the same ups and downs as any other,” she said on Wednesday.

Democrats believe her speech is more likely to be remembered for the “lipstick-on-a-pitbull” ferocity that got the Republican Right worked up into a frenzied froth. She may be compelling, they argue, but she is also palpably different and her small-town Alaska a whole lot wilder than the swing-state suburbs where this election will be won or lost.

Susan Manyoky, one of the Alaskan delegates in St Paul this week, rejected the media caricaturing her state as a place where people had little else to do but drink, get pregnant and shoot moose.

“We’re Republicans and we’re not promiscuous,” she said primly, before adding: “We do get to hunt moose and chop them up in in our basements.”

Mrs Palin has ensured that she and Mr McCain should have their own army of activists knocking on doors and waving signs for him on bridges this year. But it remains to be seen whether she repels as many voters as she attracts and proves that picking this Alaskan is half-baked.

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