We are dreaming, we Europeans, of Obamaland: a temperate land of sunshine and showers, of soft music and plenitude, of conciliation and concord. We think we caught glimpses of it in July, just fleetingly, behind the garden wall at Number 10; on the steps of the Elysée Palace, and beneath the Victory monument in Berlin, where the would-be US President finally spoke to us, before being whisked away again.

And we concealed our very slight disappointment – that he seemed so camera-shy; that even in Berlin he could not quite treat us to the same soaring rhetoric that he lavished on his fellow-citizens; that he still seemed locked in the "war on terror". But we gave him the benefit of the doubt. After all, even in Europe he was still campaigning. He had his home audience to look to, and Europe furnishes many a photogenic backdrop. We would bide our time, mouthing "Yes we can" in silent solidarity, and hope against hope for a Democratic victory.

Unless the polls are very wrong, Obamaland is materialising almost as you read. And, as we anticipate the long transition before Inauguration Day, our wish-list is almost complete. From a President who had barely travelled outside the US before taking office, we look forward to one whose peripatetic youth surely makes him a citizen of the world. From a President who believed US military superiority was there to be used, we welcome one whose stated preference is for talking first – even to adversaries -– and calling in the force of arms only as the last resort.

Download the new Independent Premium app Sharing the full story, not just the headlines

And we especially welcome someone who, even as he regrets his lack of a foreign language, seems – do we flatter ourselves? – to want to master fluent European. When the worst the Republicans can find to throw at him is to denounce his economic remedies as "socialist", is it not time to roll out the red carpet?

Europe's leaders might already be jockeying for the privilege of being first to greet the new President, but the code of Obamaland would remove the need for such undignified scrambling. The new President would be the one to hop on the plane for a lightning tour of European capitals. And this time Chancellor Merkel would have no objection to a speech at the Brandenburg Gate, especially one scripted as an apology for the Bush era mistakes and a pledge of more equal transatlantic relations ... Barack Obama has only himself to blame if he has spun dreams.

Yet all that is certain as Americans vote today is that Obamaland, if indeed it emerges from the ocean mists overnight, will not be as we imagine it. The landscape may be more familiar than the oil derricks of Texas and the barbed wire of Guantanamo, and so may be the lexicon of its leader. Perhaps, too, he might even forsake tradition and make emergency fence-mending with Europe his priority. It would be a bold overture and one that would set another tone. But Europe is deceiving itself if it believes that everything that has gone awry in recent transatlantic relations derives from the alien character and rank incompetence of George Bush.

Recent concentrated exposure to US opinion on the future of the North Atlantic Treaty Organisation – at a conference in the quintessentially English setting of Ditchley Park – suggests a startling degree of wishful thinking in Europe about the speed and direction of any change. Yes, and a reluctance to abandon long-cherished illusions. The most obvious of these is our European belief in a philosophical gulf, almost as wide as the Atlantic, between the leaders of Obamaland and Macainia as they train their telescopes on abroad. To be sure, from London, Paris or Berlin, the landscape and the language of these two Americas can look very different: one closer to our European image of ourselves, the other less so.

But the similarities are striking, and significant, too, especially on foreign policy. A President Obama is pledged to end the US presence in Iraq, but so – to a not much shorter timetable now – would be a President McCain. Internal change in Iran and North Korea may soon negate the sharp divergences that opened up between the two during the campaign. And while a President Obama has set as his absolute foreign policy priority the commitment to stabilise Afghanistan – a President McCain would also be confronted with the same imperative to avoid what many already fear could be defeat.

However consensual an approach to foreign relations the campaigning Obama has favoured, however softly he wants to speak to the European allies, he will carry the big stick commended by Theodore Roosevelt. That brings with it capabilities and opportunities that will divide the US and Europe, more than they will unite – as they have increasingly since the end of the Cold War. Barring developments unforeseen today, Afghanistan will be the first test of transatlantic relations, and it will be a severe one.

Mr Obama would not be the accomplished politician he has shown himself over the past year, if he did not exploit his honeymoon with a joyful Europe to demand a vastly increased force contribution for Afghanistan. Those countries deemed not to have pulled their weight will be called upon to do so; saying no will not be an option. Even in Obamaland it will be argued that two futures crucial to our mutual well-being are on the line: a stable Afghanistan free of terrorist camps, and the continued existence of the transatlantic alliance.

Except that it is not at all clear how far European leaders, and more particularly their electorates, will accept that analysis. Does a lawless Afghanistan represent a potential terrorist threat of such an order that a costly war has to be fought and won there? Europe has its own backyard to patrol, notably in the Balkans.

Might Afghanistan be the point at which Europe calls an end to fighting wars declared in Washington? Do we risk defeat in Afghanistan only because the terrain is tough, or because Nato, without the cold war enemy, is unsustainable?This question, lurking since the collapse of communism, will be posed with some urgency, whether Europe finds itself dealing with Obamaland or McCainia. The paradox is that a more congenial and communicative partner could foster straighter talking – and with it mutual recognition that it may be time for our two destinies to move apart.

m.dejevsky@independent.co.uk