NEW Hampshire is not the biggest place in the American union.

Tucked away in the top corner of the map, it is big enough by British standards, but tiny when set beside the continental behemoths of the south and west. New Hampshire remains, nevertheless, one of the thrawn founding democracies of the United States, and about as American as it gets.

I'm sentimentally attached to the state for reasons that have become ancient. I was first there, for a few months, in the year Elvis died. I like the reticence and austere pride of a people prone to acting – even when the act is a fraud – as though they've just walked out of a Robert Frost poem. I like the landscape, rocky and tree-covered. Last week I was childishly pleased with my New Hampshire.

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It voted for Barack Obama, handily. That had seemed no certainty, especially if you trusted the assumptions of certain pollsters. New Hampshire prides itself on an independence of mind. You can't count on it, as you can count on neighbouring Vermont, to turn out for the Democrats. You can't assume, thanks to stentorian elements in the local press, that it will favour a Republican. New Hampshire went into America's revolution with the motto "Live Free Or Die". Many of its people still believe every word.

So it re-elected Obama. That choice was reassuring in the circumstances. It put a dent in those perma-tanned Fox News faces, for one thing. But that wasn't really why New Hampshire was a small joy on election night. The state's other choices proved America is changing, changing fast and for good, and changing even in the heartland of the old republic.

New Hampshire picked a president. Then it picked its two senators, its two members of the House, and its governor. Aside from the black man returned to the White House, each of these people was a woman. While Mitt Romney was trying to turn an election into a moral auction over "women's issues", abortion above all, New Hampshire gave a typically straightforward answer. While Romney's party was trying to reassert the control of old white men over American life, little New Hampshire dissented.

For what it's worth, I owe Obama an apology. Or rather, an apology is owed to America's women, its black, Asian and Hispanic people, and its young voters. I didn't think they would do it.

It seemed impossible that their fragile coalition would form for a second time to secure the presidency of a man who promised hope and achieved precious little. White men over 45 were voting two to one for Romney on November 6.

But when I saw footage of the lines running from the polling stations, "too close to call" became a nightmare best forgotten. They were not going to take it.

What does that mean? It means they were not about to be taken for fools by a Republican charlatan. Romney's habit of saying anything, as required, destroyed him in the end. His deference to "faith-based" bigotry caught up with him. His fealty to money, power, corporate interests and barely-veiled racism lost him a race that any semi-coherent conservative should have won. America's unemployment figures alone should have ended Obama's hopes. Instead, he got his second chance.

This ought to give the right pause. Usefully, however, many among them are too demented to grasp what happened. Already they are telling themselves that Romney lost because he wasn't conservative enough, that he didn't get "his message" across, that a liberal mainstream media – in America? – poisoned the well. Above all, these cartoon zealots are refusing to grapple with the fact that their kind of politician might never be electable again.

What did voters decide? Among other things, that a $16 trillion debt must be tackled, but not while the rich are granted tax cuts, defence spending is increased, and the right's nominee is picking his next war.

The voters refused to allow the Republicans to pack the Supreme Court with ideologues liable to overturn Roe v Wade, the abortion ruling. They declined to sanction the demonisation of immigrants or the assault on gay couples. Above all, they refused to relinquish control over their own affairs.

In a rational world, Republicans would have got it by now. The vote on demographic change has been tallied. The US is these days only 72% white, if that. "Persons of colour", in that ugly phrase, increase in number by the year. They react badly to having their vote suppressed and their problems caricatured. What's more, the children of white America are comfortable, increasingly so, with diversity. They have the notion that this is what their country is, and always was, about.

Republicans put their faith in hokum instead. They think that what worked for Ronald Reagan, and what did the trick for George W Bush, should always guarantee the presidency for any well-groomed white grandfather with a self-regarding "faith" and a good set of dentures.

They want to believe that Obama was an anomaly, an aberration allowed by sentimental weakness. So they offer the wrong answers to the wrong questions.

Why was Romney even acceptable to the Christian right? Mormonism isn't just a wayward strand of old-time religion. In basic theology, it stands in relation to orthodox Christianity much as Islam stands. In fact, a conservative Muslim would have been a more logical pick for Republicans than a man wearing – I'm not making this up – holy boxer shorts.

But the hypothetical Muslim would not have been white, or a predatory capitalist, or given to asking Muslim immigrants to "self-deport" themselves.

The Republican plight goes deeper. Romney was that party's candidate, after all, because he was the least crazy of the contenders. He was the best they could come up with, the least worst of the fabricators, fabulists and true believers on offer. He said he would "create" 12 million jobs, cut taxes and throw more billions at the Pentagon than the Pentagon wants or needs. No-one in his party questioned his veracity, far less his sanity.

You could say Obama got lucky. I would say Europeans might need to re-examine their patronising assumptions about Americans.

The voters who returned the black guy no longer fit the caricatures. They are not the Tea Party (which took a hiding). They don't want foreign wars. They don't want to take abortion rights away from the victims of rape. They want their jobs back, though.

Obama has his second chance, therefore. The singular failure of the first term was his refusal to take on Wall Street, to end the tyranny of Romney's kind.

He now has the moral authority to confront that class and its hostage-taking politics. The fiscal cliff – automatic tax increases and spending cuts; good enough for Greece but not for the USA – looms. Obama should replace his "bi-partisan" nonsense with a simple statement: Who won?

He should vindicate what happened in New Hampshire and in all the stereotypical American homes. In those households, the average white man found no fault with Romney's magic numbers and cynicism. In those very same households, an average woman and her average children said otherwise. And America rediscovered its democracy.

If he wants Roosevelt's mantle, Obama had better not blow it.