America is a country of mad people governed by buffoons. That's the way a lot of Europeans are content to see it, no matter how much they love the US in other ways. A country of mad people because they are so religious, violent, overweight and in denial about things that look obvious from here but which the flag-wavers over there refuse to get. Governed by buffoons because, for the past half-century, from Lyndon Johnson to George W Bush, no US president was truly respected in much of this continent. Not even Reagan on the right or Clinton on the left. All of them, in various ways, were laughable.

That changed in 2008. With one mighty bound, the nation of mad people became a nation of visionaries, electing not a buffoon but an incredibly cool, incredibly smart, incredibly articulate leader who was so progressive and sensitive that, guess what, he might almost have been one of us. Except that, inconveniently, he wasn't. But that didn't matter. We gave him the Nobel peace prize when he'd only been in office for five minutes and drooled whenever he looked in our direction.

Now, with 15 months to go before the next US presidential election, a spectre is haunting Europe. The spectre is the possibility Barack Obama might not be re-elected. In fact it's more than that. It's the sense, among a lot of Europeans and a lot of progressives – US ones too – that Obama wasn't as great as he seemed and that, as a result, he has allowed the mad people to get their act together again and prepare to elect another buffoon next November. Prejudices confirmed. Comfort zone resumed.

That's the not-so-subtle subtext of a lot of the European reporting on US politics this summer. It's what underpins the still-not-quite-played-out European fascination with Sarah Palin, a politician who made a giant contribution to the Republican defeat in 2008 and who, if her party were foolish enough to nominate her again, would repeat the gift, even more generously, in 2012. And it's what gives so much of the discussion of the Tea Party such a hefty dose of transatlantic schadenfreude. The message to Europe from Iowa at the weekend scarcely needed spelling out. It permeated every report from the cornfields: they're so awful – and they're going to win!

Sorry to spoil the party, but almost everything about this stereotypical view of the US is both patronising and, perhaps worse, wrong. Let's put some serious caveats out there. Let's admit that the Republican right is often very dynamic and effective, admit that Obama has often failed to leverage his power as effectively as he could have, admit that Americans have become increasingly sceptical of big government and worried about deficits, and admit that, in the light of the midterm elections and with the economy sliding, only a fool would dismiss the possibility of a Republican win in 2012. Look at the polls. Seven out of 10 Americans are currently unhappy with Obama's handling of the economy. His job approval ratings have just slumped to 40%. It has to improve if he is to win.

But let's also look at a few stubborn realities that stand in the way of the self-fulfilling Republican prophesy. Let's start with the fact the Ames straw poll, last week's Iowa fundraising event, is no guide to anything except itself. It's a stunt for conservative Republicans. And it has duly conferred its blessing on one of their number, Michele Bachmann. But that's like Labour holding Barnsley.

Take note, too, of the limitations of the Tea Party. It's easy to get carried away – as Tea Party fans themselves certainly do – with the belief that they are a new force breaking the mould of American politics. But the public is becoming increasingly negative towards the Tea Party, while a new analysis published in the New York Times this week suggests the campaign is largely made up of the same old white, Christian, conservative Republican voters who did the business for Newt Gingrich in 1994 and for Bush a decade later. "The Tea Party's generals may say their overriding concern is a smaller government," conclude political scientists David Campbell and Robert Putnam, "but not their rank and file, who are more concerned about putting God into government."

This matters because, out there in the real US, real voters are not so much enthused as turned off by the overmingling of religion and politics. Yet that's what Bachmann, who holds prayer sessions on the campaign trail, offers. And it's also what Texas governor Rick Perry, the latest Republican contender to be written up in grand guignol terms, offers too. Perry may pull in supporters on the campaign trail but when he holds large prayer rallies, when he calls the head of the Federal Reserve treasonous and threatens him with a "pretty ugly" reception in Texas, and describes Obama as "the greatest threat to our country", both of which he did this week, he cuts himself off from many more voters than he speaks for.

Beware, too, of mistaking the voices of midterm US voters with those who vote in presidential years. You get a different kind of American at the ballot box in presidential years – more young voters, more black ones, often more female, certainly more liberal and more independent. You also get many more of them – one in every three Americans who voted in 2008 sat out the midterms two years later. None of this means that they will all be voting for Obama in November 2012, but if they do, the outcome will look much less Republican than it did nine months ago, when there were much higher numbers of angry white guys.

In the end, a presidential contest is about a choice between two candidates and their messages. With Republican candidates attacking each other and paying court to the party's core conservative vote, the chance that they may nominate someone unelectable would obviously help Obama. But much will also depend on his ability to re-energise the coalition, and particularly the independents, that swept him to victory on such a relatively high – by US standards – turnout in 2008. In a recession, with high unemployment and a crippling deficit, and after suffering a capricious but humiliating economic downgrade on his watch, that will not be easy. There are lots of sensible people in the US as well as mad ones. But Obama still has to win their votes.