America's 2008 election has at last come down to a national conversation about Barack Obama. When it began, 20 months ago, this was an election about George Bush, Iraq and Katrina. More recently it has become a contest about economic decline and insecurity, which explains more than anything why both Obama and his party have drawn steadily ahead over the past eight weeks. Now, having essentially decided which political offer to accept, Americans must go to the polls on Tuesday and sign off on the man himself.

That is why the argument this week, and now over the final weekend, has morphed near the end into a contest over Obama himself. Bill Clinton, as ever, posed the key question when he appeared with Obama in Florida this week. "Are you ready," he asked, "for a new president?" The Obama campaign understands this, too, just as it has understood most other things along the 2008 trail. Wednesday's unprecedented 30-minute TV election advertisement boiled down to a simple message, aimed unerringly at independents and middle-ground voters. It's OK to elect this man, it told them. It's the right thing to do.

The Republicans understand this. The final days are about Obama for them, too. It is why the McCain campaign has again turned so negative as election day nears, trying to make the Chicago-based Palestinian Rashid Khalidi into the new Jeremiah Wright or the new Bill Ayers. It is why McCain's stump speech accuses Obama of being "redistributionist-in-chief" and why supporters waved placards this week saying "Stop socialism. Vote McCain". It is why Sarah Palin, running hard with a ball that Hillary Clinton passed to the Republicans months ago, has spent the last week pitching to what she none too subtly calls "real Americans", "patriotic Americans" or "pro-Americans".

But what does it mean to say that, between now and election day, it is all at last about Obama? Travel through the US this week (as I have been doing in a series of nightly discussions on the west coast for Guardian America and the New York Review of Books), and it is impossible not to be profoundly aware that this country stands on the threshold of something that once seemed impossible. And yet when, a week from now, we reflect on the immense fact that America has elected a black president, or even if we are reflecting on the scarcely less immense fact that it has not, it will be important to remember what it feels like now - that this campaign has not fundamentally been about race at all.

Don't get this wrong. The Republicans are engaged in an "othering" of Obama into which race is inextricably woven. But the othering of 2008 is not something new and unique but something old and familiar. In 2004 they othered John Kerry as a rich liberal. In 2000 they othered Al Gore as a beltway geek. In the 1990s they othered Bill Clinton as a draft-dodging child of the 60s. Before that they othered Michael Dukakis, Jimmy Carter and George McGovern, each in his turn, right back to the othering of John Kennedy as a Catholic in 1960. Othering, in other words, is what Republicans - and sometimes even Democrats - do.

But this othering is more diabolically potent this time because it's about race, right? No, actually, that's wrong. The assumption that an inner racist demon lurks latent and uncontrollable in the souls of all white Americans, waiting to jump to the Republican dog whistle, is simply untrue. Europeans, so easily prone to condescension when talking about Americans, should not throw stones from inside their glass houses. Nor should journalists, who too often use the lazy cliche that, in the privacy of the polling booth, white Americans will do the opposite of what they say they will do.

Barack Obama is not the black candidate. He is the Democratic candidate. He is not just the representative of an ethnic group that has never even been close to winning the presidency. He is also the nominee of a party that has become something of an expert at losing it. That is the reason why, next Tuesday, American voters face a double choice - electing a president of a race they have not previously voted for; and, at least as important on the day, electing a president from a party that, in modern times, they rarely vote in.

Look at it this way. Obama may or may not have a problem getting white Americans to vote for him. But he is doing much better than most of his recent Democratic predecessors ever managed among such voters. In 2004, white Americans split 58% for Bush and 41% for Kerry. Four years before that, they went 54% to Bush and 42% to Gore. In 1992 Bill Clinton had a two-point lead among white people. Four years before that, George Bush Sr beat Dukakis by 20 points. Against that historical backcloth, Obama's one-point lead over McCain among white voters in the most recent New York Times-CBS poll looks pretty significant, while his bigger leads among white women, white men under 45 and, especially, white independent voters look potentially like a set of decisive turnabouts from recent Democratic experience.

In fact, if you are looking for one theme from late 20th-century elections that marked American contests out from western European ones, it was not the politics of race but the politics of gender. For much of the past century in most European industrial nations including Britain, men tended to vote to the left of women, though that has begun to change recently. In the US, by contrast, women have in recent decades tended consistently to vote to the left of men. That certainly makes white men - who are around one in three of all adults - a key group of voters next week. But the fact that Obama is polling more or less even with McCain among them looks like a strength, not a weakness.

Yes, there is a lot of evidence from things like implicit association tests that racist assumptions still lurk in millions of white American minds (and European minds too, of course). But that doesn't mean that racism is the only thing you need to know about such people, or that it dominates their minds, or that they are incapable of overcoming it. In particular, it doesn't mean that, when asked to vote for this black man at this time, they will not do so. Americans have spent a long time getting to know Barack Obama. The evidence is that they like what they see, and that they are about to do something both right and great.

martin.kettle@theguardian.com

· This article was amended on Friday November 7 2008 to correct information about how white people voted in the previous five US presidential elections. The Republican and Democratic shares of the vote among white voters were: 60%-40% in 1988, 41%-39% in 1992, 46%-43% in 1996, 54%-42% in 2000 and 58%-41% in 2004. In addition, Rashid Khalidi's name was misspelled as Khalili. This has been corrected.