America doesn't have a class system. That's a European thing, right?

Here in the Land of the Free, you can be born in a log cabin you helped to build, overcome poverty and pull yourself by your pioneer bootstraps – all the way up to the White House. Or even Wall Street.

Despite a shed-load of evidence to the contrary, many still swallow this New World fairy tale. Rick Santorum is one of the few Republican candidates warning that economic mobility in the US lags behind western Europe. Nevertheless, debating his Republican rivals before the New Hampshire primary, the former senator got positively hostile over all the talk of "middle-class" hardship, claiming that merely using the c-word somehow "buys into the class warfare arguments of Barack Obama". With all the certainty of a man who refuses to believes in evolution, Santorum said, "There are no classes in America."

It would be pretty to think so. However, the reality is that America is more class-bound than other advanced nations. If you really want to achieve the American Dream, move to Denmark. A child born into the bottom fifth on the income scale in Denmark will almost certainly better his economic situation: only one quarter of those at the economic thin end stay there. The same is true of other Scandinavian countries.

Britain, with its royals and its rituals, its titles and its toffee-nosed traditions, has always been the class system poster child for Americans (I'm looking at you, Lady Mary Crawley!). We're hooked on the upstairs-downstairs exotica of Downton Abbey, yet Americans should know that people in the UK have a greater chance than we do of improving their financial circumstances – 42% of Americans never escape the lowest income bracket, compared to 30% of Brits.

A recent report from the Pew Charitable Trust's Project on Economic Mobility confirms what previous studies showed: if you're born into the underclass, you're likely to die there, as stuck in your station as a Victorian housemaid. Similarly, if you're born to highly-educated parents with a fat stock portfolio and a house in the Hamptons – or maybe if your mother is a member of Congress (over half of them are millionaires) – your grandchildren probably won't have to sweat the school fees or the holidays in St Barts.

American income inequality is becoming positively third world, with some of the richest US states having the largest populations of poor people. In California, 22% live in poverty. In Florida, it's 20%. The citizens are getting restless. The Pew study also shows that two thirds of all Americans think social inequality is more damaging to the nation than racism.

The question is, what will we do about it? Or, more specifically, what will President Barack Obama and Mitt Romney (the Republican presidential nominee-presumptive) do about it?

Campaigning in 2008, Obama didn't like to talk about class. He embraced American optimism (all that "hope") and unity, proclaiming "there's not a conservative America and a liberal America, there's the United States of America." Inspiring, if largely inaccurate. These days, the excesses of the 1%ers are so egregious and in-your-face that it would be political malpractice to ignore them. Obama has taken to pointing out that those who created much of America's economic success don't benefit from it; now, he says he's a "warrior for the middle class".

Romney is still trying to win votes from Tea Partiers, Southern Baptist supply-siders and readers of Ayn Rand comic books. So far, he's had a tin ear for the country's anger. In Iowa last summer, he snapped at a heckler, "Corporations are people, my friend."

Unlike Santorum, Romney name-checks the middle class, even claims to be part of it. You know: just a regular guy who happens to be worth more than $250m. He complains that making an issue of income inequality plays into the envy raging in the breasts of the less-favored. He told an interviewer:

"The president has made it part of his campaign rally. Everywhere he goes we hear him talking about millionaires and billionaires and executives and Wall Street. It's a very envy-oriented, attack-oriented approach." Romney's solution? "I think it's fine to talk about those things in quiet rooms."

Of course: like gentlemen, perhaps in the Grill Room at the Harvard Club, over a Cognac and a Cohiba.

America isn't about to erupt in a full-blown class war: our revolution didn't pit the peasants against the aristos; it was the bourgeoisie (led by plantation owners) versus the taxing authority of the king and Parliament. Nevertheless, we've started using the language of the sans culottes. The right wing accuses Michelle Obama of behaving like Marie Antoinette whenever she wears a new dress, and charges Barack Obama, with his Ivy League degree, with being a card-carrying member of the hated "elite". Progressives counter that Mitt Romney was born into privilege and – far worse – made millions as a "vulture capitalist" on Wall Street.

Romney's Republican opponents have painted him as a heartless rich boy thoughtlessly shutting down factories and throwing people out of work. No doubt, the Democratic party will write them a nice "thank you" note later. Romney's new strategy is the Tea Party's old strategy: Obama isn't a real American. At his New Hampshire victory speech, he claimed that Obama "takes his inspiration from the capitals of Europe", instead of "the cities and small towns of America", and wants to transform the country into a "European-style entitlement society". (It's weird: first Republicans said Obama was African, now he's European. If he's not careful, they'll eventually decide he's really just another white guy.)

If nothing else, this election might get Americans to admit that, yes, we have a class system, no matter how much we try to deny it. Writers have been trying to tell us about it for years, we just didn't listen. Here's Kurt Vonnegut describing it back in 1965: