The morning after Barack Obama's re-election, panic broke out. Radio 4 described financial markets slumping on worries over something called a "fiscal cliff". The New York Times, normally drunk on its own sobriety, warned of a "looming fiscal crisis". Other newspapers and TV networks predicted an economic "abyss", "peril", even "imminent armageddon". And that was before you got to the blogs.

The clock is ticking, apparently. Obama has until New Year's Eve in which to strike a deal with the Republicans – otherwise nearly 50 tax cuts will expire and the defence department alone will get slapped with $1.2tn in cuts. Unless the Democrats give the Republicans what they want in the form of further tax giveaways for the richest, the senator Mitch McConnell and his rightwing allies will block any attempt to extend borrowing – with disastrous economic consequences. It sounds like a budgetary version of the film Speed; but this is the fiscal cliff Washington is driving off. And the result will be another recession in the US (and, more likely than not, around the world, too) and soaring unemployment. No wonder ABC News calls it "taxmageddon".

There is just one problem with this version of events: it's exaggerated. Distorted. More spiced-up than a bargain balti.

For a start, the very term is wrong. Even if the most bloodcurdling predictions are borne out, there will be nothing cliff-like about 1 January 2013. Americans are not about to have a collective Wile E Coyote moment, in which they suddenly find themselves paddling furiously in mid-air – before the inevitable descent begins. This isn't a cliff-edge at all; it's more of a slope.

Over a full year, the measures surely will be devastating (enough, predicts the Congressional Budget Office, to see the US economy go from growth of more than 2% this year to shrinking by 0.5% next year). Most recipients of a payslip will not immediately clock that they are paying a bit more in tax – although they certainly will over the course of a year. But that gives the Democrats plenty of extra time to come up with their own proposal for a deal and haggle with the Republicans.

Yet metaphors matter; and so does media noise. Making out that some indescribable calamity is already inked into the calendar allows the right to hijack the Democrats' budget plans even before Obama begins his second term in office. Britons have had some experience of this.

After the general election of 2010, as Labour, the Tories and the Lib Dems negotiated over who would form a government with whom, the press and commentators in financial markets colluded in the pretence that the Great God of Gilts had no time for democratic deliberations. Nick Robinson was on TV heckling Lib Dems: "Are you not in danger of playing both sides while the country waits and the markets quake?"

And then, when Cameron and Osborne were safely installed in Downing Street, they regularly warned that unless historic cuts were laid out now, the markets would treat Britain as callously as Greece. The results we now know: businesses and consumers sat on their hands; tepid recovery was snuffed out; Britain went back into recession, and even now our annual national income is some 5% below what it was before the crisis.

Democratic debate was railroaded; the wrong economic policy was followed – and it was all done to avert a wildly inflated threat.

Something similar is happening in the US this time. Not everything is the same, of course, since history rhymes rather than repeats. So the argument in the US is about avoiding having too small, rather than too big, a deficit next year; even right-wing Americans acknowledge that severe and sudden austerity would be disastrous.

But the budget hawks in the US do want Obama to accept austerity over the longer term; and, what's more, they have plenty of money behind them. One of the major figures in that debate is the private-equity baron Peter Peterson, who has his own foundation and is pumping in millions to push for a "grand bargain" in which the Democrats are forced to slash social security and health spending to avoid the fiscal cliff. With that much money, he has plenty of allies in Washington, too – including former Clinton White House official Erskine Bowles, who is now being talked of as a possible new treasury secretary.

I can only hope that America's Democrats learn their lesson from the British experience. Because the right here owned the language and framed the debate. But that wasn't enough to defy economic reality.

The US, like the rest of the west, needs to have a serious debate about its long-term budget outlook. But that needs to take into account how to reduce its debt fairly and sustainably and in a way that allows for growth. Exactly the debate that, two years into its austerity government, Britain is still waiting to have.