OCCASIONALLY it is tempting to do what no rational person ever should and echo the words of Lincoln Steffens Esq.

Mr Steffens, you will recall, was the reporter who returned from Soviet Russia in 1919 to declare: "I have seen the future, and it works." It didn't, of course, and tens of millions paid the price in lost or miserable lives.

Mr Steffens's words were fairly shouting down the decades, though, as the pictures came through from the US presidential election. Where to look first for a sign of things to come?

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Was it the crowd of ecstatic Obama supporters outside the White House: young, black, white, Latino? Or the disappointed Republicans, invariably Wasp and waspish, waiting for Mitt Romney to concede?

Political romantics might have opted for the sight of Joe Kennedy III – Bobby Kennedy's grandson – being elected to Congress. Already Kennedy Jr is being asked if he wants to run for the presidency one day. Poor kid.

Was it the election of the first openly gay senator, or the trouncing of Republican candidates who want to take women's reproductive rights back to the Stone Age?

All signs and wonders, but the smart money should have been in Chicago at President Barack Obama's victory rally. Ostensibly the man of the moment was Mr Obama, winning a second term against all the economic odds. But the real glimpses into the shape of America's political future were arm in arm with him – his wife Michelle and their two daughters.

With women representing 53% of the electorate in the 2012 election, the future is female. Add non-white, young, aspirational and progressive, and you begin to build a picture not just of the America developing before our eyes, but of the kind of voter the Republicans must start to court. Adapt or die – it's as brutal, as Darwinian, as that.

Not that this will be the first instinct of the Grand Old Party. They will point to the close popular vote, 50% for Mr Obama, 48% for Mr Romney, as proof they were on the right track. Hence the tweets from Donald Trump who, like Karl Rove on hearing Fox News pundits calling the election for Mr Obama before all the votes were in, "spat out the dummy" as we say in these parts. "This election is a total sham and a travesty," opined Mr Trump. One looks forward to The Donald renouncing his American citizenship and seeking asylum in his beloved Scotland.

But focusing on the popular vote alone misses the point both about how politics in America has changed from macro to micro, and how the electorate has changed. Mr Obama won not because of great ideas or an outstanding record in office, but because he got the vote out in the states and the streets where it mattered. And he got the vote out because his teams knew, right down to the last detail on the database, who these supporters and undecideds were. While the Obama machine was plugged into the electorate, the Romney camp was still searching for a socket.

The election numbers illuminate how the US has changed, and what a winning coalition of American voters in the early half of this century looks like. Mr Obama scored majority support among Hispanic, Asian, and black voters. He won among the 18 to 29-year-olds and the 30 to 44-year-olds. Crucially, he won 55% of the female vote compared to Mr Romney's 44%. Women voters outnumbered male voters by 10 million. Of that female vote, Mr Obama won a majority among mothers and single women.

What the Republicans have to ask themselves is not how much further to the right they should now go, but how they can better appeal to this new mainstream America. In each case, however, they face formidable obstacles. They could go after the Latino vote – set to increase from 16% today to 30% by 2052 – by adopting a presidential candidate from that community. There are enough capable individuals ready and waiting, such as Marco Rubio, the Cuban-American senator. But as long as the party remains overwhelmingly white and overwhelmingly hostile towards immigration, they won't convince the majority of Latinos or Asians that the party is on their side.

As for women, one has looked at the Republicans throughout this long campaign and despaired. Faced with Freud's question, what do women want, the GOP doesn't have a clue. There were Freudian banana slips all over the place, from Mr Romney and his "binders full of women" to congressman Todd Akin and his theory about "legitimate rape" not resulting in pregnancy because a woman's body would naturally "shut down".

Even when the party tried to play nice, by bringing on the wives to speak about how wonderful their husbands were, it was a move as out of its time as girdles and beehives. Regardless of what some Republicans would like, the clock is never going back to the 1950s. Those fabled "homemakers" Mr Romney tried to court are also likely to be working women, as concerned about the economy as they are about health, as unwilling to be lectured on their bodies as about how they spend their hard-earned money.

The lesson many have been quick to draw from this election is that America is a divided nation and neither camp is for budging. That has always been America, some will say. It has been split on and off since birth, and its political system reflects and encourages that. Stalemate is the safest state. But what a dismal future that conjures up. The victorious Democrats today could be the defeated Democrats in four years, by which time, if nothing is done, the divide will be deeper and more bitter.

Both Mr Obama and Mr Romney know this. Each man said a lot of suitably warm words about bipartisanship when the contest was over. How long the mood will last no-one knows, but it would be a safer bet to opt for days rather than weeks. There is nothing a wounded and angry Republican party would like more right now than to see Mr Obama go head first off that looming fiscal cliff.

One hopes wiser heads prevail. One hopes the Republicans look, in particular, in the direction of Michelle Obama and what she represents. America has changed. The great tragedy of the Republican party is not that it didn't change, but that it did so in the wrong way, becoming more extreme and less relevant to most people's lives. America, the Michelle Obamas of America, left it behind. They don't miss it a bit, but democracy will.