How the East was one: The incredible comeback of Hillary Clinton

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As supporters and volunteers trickled in to the vast sports hall of Southern New Hampshire University on Tuesday night, the electronic scoreboard showed two names where two competing teams would normally be displayed – "HILLARY" and "CLINTON". Anything to lift the spirits on a night not expected to be fun. Only the superstitious or deliriously optimistic among the early crowd would have taken this tiny gesture as any kind of omen for how the night would turn out. The pundits and the pollsters had called the Democratic primary here already. It was Barack Obama's to lose. And that wasn't going to happen.

How fast things change, how fickle the voters and how cruel the sport of politics. The hall never did fill up – nobody likes a wake – but the reward for those who came was grand. It was the ticker at the bottom of the CNN results broadcast on the projection screen that kept them abreast. As the numbers adjusted and Clinton's narrow lead held steady, their lungs grew deeper and the screams louder.

As sheer thrill began to suffuse the cheeks of young Clinton staffers, journalists battled puzzlement. On the whole they don't like it to be assigned to the losers' camp on election night. So this was starting to look good. But surely, the numbers would flip. Where were the results from the big university towns? Fox News had an exit poll showing Obama still winning. Hold tight, it will change.

Or not. The networks declared quickly for John McCain for the Republicans after polls closed at 8pm (1am Wednesday GMT), even though his edge over Mitt Romney was not huge. But the Democrats had a long wait before the reality of what had happened in precincts up and down the state became clear. Clinton, against all apparent odds, had prevailed. And it was women what did it for her. And her not-quite tears. It was much later, already 10.25pm, when Terry McAuliffe, Clinton's campaign chairman, finally showed up to begin making the rounds of reporters. He looked six inches taller.

"We have a pretty good idea of what is going to happen," he admits to a small gaggle by the over-used bathrooms. He was opening his mouth to answer the next question – how pivotal had been that moment on Monday when Clinton became uncharacteristically emotional on the campaign trail? – when a Vesuvian eruption explodes down the corridor. NBC had moved first. Hillary wins!

Moments later, Hillary pops up like a rabbit amid the sea, if not ocean, of loyalists. She is natty in a grey top with black brocade, but her rival John Edwards, a distant third on this night, once got in trouble during a debate for remarking on her wardrobe. It seems sexist. To focus on the fact she is a woman, however, is legitimate tonight. A vulnerable woman, indeed. Here, "Hillary Has Feelings" is the headline.

By this reporter's count, she mentions "heart" three times in roughly the first three minutes of her speech. Her inevitable "Comeback" line came quite a bit later. "With a very full heart," she says near the top, "I came to New Hampshire to listen to you – and in the process I found my own voice."

What happened in this state to rescue Clinton's bid for the Democratic nomination will be pondered for a very long time. But no one in her entourage doubted yesterday that that moment on Monday in a Portsmouth café when she answered a question about the sheer human effort of hitting the campaign trail each day – especially after her third placing in Iowa last week – had had a pivotal impact.

"It's not easy, and I could not do it if I just didn't passionately believe it was the right thing to do," Clinton responded that day. Lowering her voice almost to a whisper and with eyes that seemed wet, she went on: "I have had so many opportunities from this country. I just don't want us to fall backwards."

Confected for the cameras possibly, but for a few seconds Clinton, normally so reserved and controlled, seemed to emerge from her bubble of scripts and talking points.

Possibly, it resonated with women voters especially. Exit polls show us that women overwhelmingly chose Clinton over Obama, particularly young women with no children. In Iowa it had been Obama who won the support of most women. People got to see the Hillary Clinton I have known for 25 years," Mr McAuliffe said of the café scene. "A woman who cares deeply about the issues and someone who is going to deliver on the issues."

Women voters may also have connected to Clinton on the big television debate night last weekend when the moderator suggested she was not widely liked. "You have hurt my feelings," she said, but smiled.

More must have gone on, however, for her to turn the tables on Obama so comprehensively. His was meant to be the "big mo". But the momentum paradigm has shifted now. Now it is hers.

But the next big test is the Democratic primary in South Carolina, with a huge pool of black voters, on 26 January. He may win it back. The battle for momentum – and eventually the nomination – is only beginning.

One early instinct is to berate the polling industry. They regularly get election outcomes wrong. But rarely are they so far off course as in New Hampshire, with most surveys giving Obama a double-digit gap over Clinton, even on Tuesday. Are their methods faulty? Or were respondents dishonest?

Several factors should have told us not to trust predictions here. The voters of New Hampshire have a reputation for bucking both what happens in Iowa before and what the world expects of them.

There is also the heavy presence of independents in the state, who are particularly apt to switch candidates – even parties – at the last moment. Indeed, a University of New Hampshire poll on the eve of the vote showed 20 per cent of voters undecided and another 24 per cent only "leaning" towards one person.

"Polls always overstate the degree of commitment voters have to their vote... The fact is, going into the election, there were still many people who were undecided – about half the electorate had not firmly decided," noted David Moore, a veteran polling analyst based in New Hampshire and author of the forthcoming book The Opinion Makers: When Media Polls Undermine Democracy.

But the elephant in the room here may be race. That would be Obama's race. Did he slip back because of what some call the "Bradley Effect", a phenomenon that traces back to the bid by Tom Bradley, an African-American, for the California governorship in 1982. He was placed to win that contest by the polls. On voting day, however, cold feet took over.

And New Hampshire, the last state to recognise Martin Luther King Day, is very white. Yet so was Iowa and nothing of the sort apparently happened there.

In New York yesterday, Obama recognised that elections can always end in surprise. "Anyone who thinks they know how voters are going to respond at this point are probably misleading themselves," he said. "And I think voters are not going to let any candidate take anything for granted."

Reacting to his third place finish, John Edwards said: "Up until now, about half of one per cent of Americans have voted. Ninety-nine per cent plus have not. And those 99 percent deserve to have their voices heard because we have had too much in America of people's voices not being heard."

Yet to focus too long on undecided voters and polling errors would be to underestimate other realities. They include the weaknesses in Obama's candidacy, inspiring though he may be. Nor should we overlook the firepower and deadly accuracy of the Clinton campaign. And then there is Bill.

Hillary Clinton repeatedly in New Hampshire implored voters to weigh her experience over the relatively tender years of Obama. Anecdotal evidence suggests this stuck with some voters, who chose head over heart at the last moment. This may have been especially true when it came to the economy. Exit polls showed many more voters showing faith in her in this regard rather than him.

The marriage of Hillary and Bill – romantic, perhaps, political, certainly – is the stuff of myth already. In New Hampshire, the dividends may have turned out to be huge. Voters remember the scandals for sure (and, by the way, remember the dignity of Hillary in enduring them), but they remember something else about the Nineties. Bill Clinton did make the economy work better. When the issue was the economy, voters ran not for Obama but with Hillary.

Bill was complaining here that the short time between Iowa and New Hampshire was unfair, because Hillary had too little time to challenge the heartland bounce of Obama. But maybe five days was just, by a whisker, long enough. Bill played his part well. "Give me a break," he declared angrily about Obama's record regarding the Iraq war. His version, he said, was a "fairy tale". Someone listened. Hillary, by the way, was allegedly not quite as surprised yesterday as the rest of us. Even on Monday night, a campaign source said, she was telling aides that she felt a change in the tide. Yesterday, at home in Chappaqua, New York, she added: "I really believed I had a very good chance. Nobody else believed it. But I did, and I'm very grateful to the people of New Hampshire for giving me victory last night."

Now we will see what steel Obama has. He may one day be grateful to New Hampshire. It has given him a jolt. He knows a bit better now what he must do before the next big vote in South Carolina in two weeks. Expect big speeches on the economyand foreign affairs. The charge against him that he is unspecific on issues is not fair. But he must do a better job of telling voters that. One consolation for the Obama campaign scrap-book. History books may show that Marianne Pernold Young, 64, who asked that single question in the café on Monday may have single-handedly delivered New Hampshire to Clinton in 2008. But guess what. She voted for Obama.