Spend a few weeks following the leaders of the three main parties and you soon realise that – regardless of the results of tomorrow's vote — a hierarchy has emerged in this campaign. When Gordon Brown turns up somewhere, he's lucky if there's more than a smattering of party faithful ready to greet him, perhaps two dozen souls holding the odd placard. That could be a function of his security arrangements, with details of his travel not released in advance, or it could be a commentary on his public standing. But the harsh truth is that a visit from Brown generates little hoopla.

Next up the pecking order comes David Cameron. There's always a healthy number of people at his events, usually arranged photogenically – white men in suits nudged out of shot; those who are young, female, black or Asian ushered to the front – and reliably ready with a cheer. But the suspicion lingers that the crowd has not exactly gathered spontaneously, that it has been convened through diligent advance work.

And then there's Nick Clegg. When he pops up, there can be up to 400 people waiting for him – even on a rainy morning in Lewisham, south London. Sure, that's a tribute to the Liberal Democrats' famous knack for pavement politics and, admittedly, the local party had a week to organise its people. But that doesn't explain the large number standing in the cold who are neither party members nor even past Lib Dem voters. Nor does it explain the crowd of onlookers across the street, waiting for the speaker to arrive, nor the people in the flats overlooking the common who open their windows to see the show.

Judged by the unscientific measures of crowd size, enthusiasm and head-turning interest, Clegg is the undisputed star of this campaign. He managed to pack out a meeting hall in Redcar on a grey, chilly Sunday night – a feat for any politician and a serious achievement, in the ancestrally Labour north-east, for one not wearing a red rosette. It's hardly a surprise that he all but stops the traffic in leafy Richmond, south-west London, a seat the Lib Dems already hold. But here he is at the centre of a giant scrum of press and public, as he tries to squeeze his way into a packed community centre in Labour-held Streatham.

In little over three short weeks, Clegg has gone from a face barely recognised outside the Westminster village to a phenomenon. Where once his party had to beg for attention, he now has to fend off questions not just from a British press pack at last treating the Lib Dems with respect, but from CNN and a clutch of other foreign reporters, who have made the trek to see the man who threatens to reshape British politics.

The size of his personal protection detail has gone from negligible to serious, men with discreet lapel badges shielding him from the jostling throng whenever he steps off the battlebus and on to the streets. When his wife, Miriam González Durántez, is in tow, she has to handle a Spanish-language press corps of her own. These are not scenes that accompany either Brown or Cameron.

For old time Lib Dems, this is all something of a shock. "There's a groundswell that we've never seen before," says Michael Chuter, a party member in Lewisham since the last great moment of Liberal opportunity, back in the hung parliament days of 1974. In Richmond another veteran, Geoffrey Morgan, 79, admits that he's more of a Vince Cable man, "but that's because I'm old". Look, he says, pointing at the rows filled with eager-eyed first-time voters, teenage faces who, in Morgan's long experience, had never been seen at Lib Dem meetings before. "He attracts all these youngsters," he says, marvelling at the novelty of it.

This has prompted Clegg's more hyperventilating supporters to hail him as the British equivalent of a certain US president also blessed with a knack for reaching those whom politics had never touched before. Glen Neil, the dreadlocked director of the Palace Project, the community centre that hosted Clegg in Streatham, makes the comparison, speaking of "the Obama effect".

Riding the wave, the former Play School presenter Floella Benjamin introduces Clegg as if he were indeed about to work Obamaesque miracles. "There's a man who's worked hard to wake up the people of this great land – a great man, who has vision, who puts children first, who has a beautiful wife …"

The Obama parallel is ridiculous of course: the path that carried the young and privileged Clegg from Westminster School to Westminster is hardly comparable to the "improbable journey" that took Obama to the White House. Clegg's rhetoric rarely aims for the poetic or the soaring, knowing that in a British political context that would often be plain embarrassing. But there is one thing the two do have in common.

Clegg scores by seeming utterly sincere. Here again, a hierarchy emerges. Brown struggles to communicate in plain, human English; Cameron is better, having mastered the simple, fluent sentence, but leaves doubts as to whether his words are merely those of a slick salesman. Clegg is just as fluent as Cameron, his sentences, if anything, even more colloquial and easy to understand. But he has one great advantage over his Conservative rival: no one so much as raises the question of his sincerity. He is assumed to be completely genuine. The latest Guardian/ICM poll found just 17% regarded Clegg as a creature of spin, fewer than half the 38% who believed that of Cameron. Of the three party leaders, voters say Clegg is the least spun.

This is what he shares with Obama. As a candidate, Obama was universally admired as a brilliant communicator. But what made him a phenomenon was people's belief in him: they thought he was for real. It is what gave Clegg his edge over Cameron in the debates and what people seem to respond to when they meet the Lib Dem leader in person. Partly it's his tone of voice, sometimes exasperated, as if straining to make his case. To some ears, that might sound like impatience, even irritation – the tone of a man who does not suffer fools gladly. But others seem to hear it as a token of his conviction.

He also deploys colloquialism to deadly effect. In the TV debates he branded Cameron's rightwing European allies as "nutters". That cut through, because it seemed to cast Clegg as a rule-breaker, a maverick unbound by the conventions of polite political society.

On the road, he does the same thing. Asked by an unemployed woman about the rate of the jobseeker's allowance, he comes back with: "JSA's now, what, 52 quid?" That use of "quid" would never come out of Brown's mouth. If Cameron said it, it would sound like the master coming down from the big house to address the cotton pickers. But Clegg gets away with it, sounding like a regular bloke rather than a politician. Asked yesterday by Jeremy Vine about various hung parliament scenarios, he complained such talk "does my head in".

His stump speech is full of such phrases, channelling the frustration voters feel in language they themselves might use. "I don't understand the point of strategic health authorities," he says, apparently baffled. "I don't understand the point of an NHS computer system that doesn't work." These don't sound like talking points he's mastered, but like genuine cries of irritation uttered as if for the first time. That they appear in his stump speech again and again is noticed only by the press corps that follows him – who could give parts of the speech themselves, in their sleep.

One of the feelings he stirs is unexpected: it is relief. For a certain kind of progressive voter – call them the Guardian reader – Clegg voices exactly what they think, but rarely hear from a mainstream politician. So they applaud when he denounces the "illegal invasion of Iraq". They cheer when he promises to lift the "dead weight of debt" left around students' necks by tuition fees. They clap when he defends offshore windfarms, not only on environmental but aesthetic grounds: "They're rather magnificent actually, tall as the Eiffel Tower, blades as big as the London Eye." Add to that his ability to conduct interviews in at least four European languages and his eloquent recent essay in praise of Samuel Beckett, and you can see why many in the Guardian/Radio 4 demographic are swooning.

That said, he has run a far from flawless campaign. He lets his irritation show too easily, denouncing hostile questions from voters as "ludicrous" or "absurd". He prefers the students in their "I agree with Nick" T-shirts.

But his much larger mistake relates to his message. On 25 April he allowed Andrew Marr to lure him into a question on process, hinting that he would not work with Brown should Labour come third in the popular vote. Ever since, he has been asked about little else. Interviews that should have focused on Lib Dem plans for fair taxation or the green economy have instead been attempts to coax Clegg to lean towards either Brown or Cameron as putative coalition partners. It's only a theory, but it's possible that that diversion from the Lib Dem policy "offer", and on to prospective horse trading, may account for the plateau the party hit in the polls soon after the first TV debate had pushed them so high.

Clegg was at it again yesterday, with an FT interview that seemed to tilt favourably in the Tories' direction – and also to soften what had appeared to be the hard, non-negotiable Lib Dem precondition of electoral reform. Even if another interview comes soon, tacking in the opposite direction, it still represents precious airtime Clegg has spent not winning votes.

That said, few in his own party or outside it will criticise Clegg for what he's achieved in this remarkable campaign. It's not just that he put 10 points on the Lib Dem poll rating in a single night. It's that he stole "change" from the Tories and "fairness" from Labour, offering himself as the agent of both.

And somehow, in the process, he became the first leader of the Lib Dems – a party associated for years with sandals, lentils and beards – to shine with a little stardust.