They truly expected Mitt would win. Not just the right-wing talk-show hosts and the dedicated Republican pundits living in their parallel universe, but the top campaign brass, even the candidate himself, who had prepared only a victory speech. That incidentally may explain the brevity and grace of Romney's concession in Boston on Tuesday night. In the event, nothing became him in defeat so much as the way he took it.

And it wasn't just a defeat, it was a big one, whose dimensions were a surprise even to many Democrats: over 2 per cent in the popular vote and a crushing 332 votes to 206 in the electoral college, in what is supposed to be a 50/50 country. And this in a year when the struggling economy was the main issue, and Republicans were fielding a candidate whose selling point was his economic and business expertise. What went wrong?

The initial reaction, as with a patient who is told their illness is terminal, was denial. Nothing was wrong, some of the true believers said at first; after all the party had kept control of the House of Representatives. The problem had been the dastardly negative tactics of the opposition ("Obama succeeded by suppressing the vote," blathered Karl Rove, one-time campaign guru of George W Bush). Others blamed the electorate: "We don't need to change to appeal to voters," insisted the conservative talk-show host Laura Ingraham. "We need voters and their mindsets to change."

But this weekend, cold reality is sinking in. One sign is the fact that almost no one is blaming Romney himself for the defeat, or evoking other, better candidates who might have won. Normally the knives would already be out, and until the very last weeks, Romney indeed waged a poor campaign, passive and gaffe-prone. But if anyone is being made scapegoat, it is New Jersey's Republican governor Chris Christie, guilty of actually praising President Barack Obama's response to Hurricane Sandy. But the problems run far deeper than one or two individuals, or a storm that arrived at the worst possible moment.

The Republicans lost because America has changed, and the extreme conservatism they currently expound has indeed lost its appeal. As everyone points out, correctly, it is a matter of demographics. The archetypal Republican voter is older, white, male and non-urban, at a time when the country is more diversified and urban than ever, and when the votes of women and Hispanics – two constituencies whom the party this time seemed to go out of its way to alienate – have become crucial.

Why has Virginia, until recently a Republican banker, twice voted for Obama? Because of the younger professionals and minority voters who have flocked to the booming Washington DC suburbs, outnumbering traditional Republicans in the state's less populated heartland.

Amazingly, President Obama even carried the Cuban-American vote in Florida. Steve Schmidt, a top adviser for John McCain in 2008, put it neatly: "In 1988, 60 per cent of the white vote won George H W Bush a landslide. Now that only buys a sizeable defeat." In short, Republicans have to remake themselves. But their sickness is not terminal.

Yes, the challenge is at one level daunting. But it is also pretty straightforward. What Republicans must do has been done by other parties, both in America and elsewhere – and relatively quickly. Not long ago, the Democrats drifted left, forfeiting the centre, and as a result lost three straight elections in the 1980s. But Bill Clinton hauled them back to relevance, and the party has won the popular vote in five of the six elections since 1992. In Britain, Messrs Blair, Brown and Mandelson did much the same with New Labour.

Not only are some specific remedies obvious (a more accommodating immigration policy to woo Hispanics, less of the wild talk on abortion that so repels women). No less obvious, the party must regain the centre. Not by coincidence did the late surge that convinced the faithful of a Romney victory come precisely when the candidate started to sound more moderate.

Best of all, Republicans have a strong line-up of potential leaders to implement such changes. Mitt Romney was a transitional figure, an unconvincing bridge between unlamented George W Bush and this new generation – Paul Ryan, Marco Rubio, Bobby Jindal and Christie the turncoat to name but four. By common consent, they are more impressive than anything in the Democratic locker (Hillary Clinton, of course, could change things.)

The real issue is not identifying what needs to be done. It is whether it can be done, given the way a nominee is chosen. Think back to the Republican primaries. Why was the field so weak for an eminently winnable election, given the state of the economy? Simply because many of the party's more credible figures refused to put themselves through a process where they would be forced to appease the social and fiscal arch-conservatives, who dominate the primary electorate and the kingmakers on the talk-show circuit.

Romney chose to jump through the hoops. He proclaimed himself a "severe conservative". His hand shot up in assent when asked if he would reject a deficit-reduction package that contained one dollar in tax increases for every 10 in spending cuts. He came out in favour of "self-deportation" for illegal immigrants. In doing so, he destroyed himself. Not so long ago, a Republican nominee could talk conservative in the primaries, then tack back to the middle ground for the general election. Now it's just too much of a stretch.