The challenger for his country's highest office decided to offer a statement of philosophical principle.

"We can't," said Mitt Romney solemnly, "kill our way out of this mess." The world beyond America's shores no doubt allowed itself a small sigh of relief.

The former governor of Massachusetts did claim, however, that a non-lethal United States would require still more defence spending under his leadership. While reducing its gargantuan deficit. While growing the economy. While creating 12 million jobs. While causing real wages to rise. And while imposing no burdens on anyone in the Romney income bracket.

It mattered little that the US already spends more on its military – as the governor's opponent pointed out – than the next 10 nations on the planet. It was irrelevant that its supposedly shrunken navy outguns the next 13 possible challengers combined. It didn't count that, as Barack Obama also observed, the always-voracious Pentagon doesn't need or want the largesse Mr Romney promises.

Here was the strange, fuzzy logic of a presidential election, a moment in freeze-frame from the third and final debate between the candidates whereby voters could be enlightened and informed. Why strange? This was Mr Romney, all agreed, moving to what counts in American politics as the centre ground.

It is an easy place to reach. The latest lurch from the Republican challenger amounted to nothing more than acknowledgement that wars are best avoided. Beyond that, Mr Romney wanted only Mr Obama's policies with additional firepower in reserve. The centrist position, it seems, is to curb Iran, control the Middle East, quit Afghanistan and defer always to Israel. The rest of the world barely rates a mention.

This is worth remembering. Understandably enough, the US electorate is obsessed with the economy and at odds over social policy. Its interest in "overseas" extends no further than the preservation of American lives and the repatriation of American jobs. Its two possible presidents therefore speak the same vague language: exceptionalism, leadership and what Mr Obama called the "indispensability" of the US in the affairs of others. It means little to Americans and it will not decide the election.

Two facts are now commonplace. One, endlessly repeated, is that the contenders are neck and neck. The thoughts of handfuls of undecided, non-aligned citizens in Dayton, Ohio, or St Petersburg, Florida, are paramount. A few counties in a few swing states, nine at most, will decide the race. Mr Obama is thought to have an edge still in such places, but a larger truth is at stake. Yet again, the vast majority of those liable to vote in a multi-billion dollar election – 60% or so – are split down the middle.

Hence the second fact. Had Mr Obama been facing a Republican who was better trusted, even slightly consistent, or capable of offering a plausible conservative alternative, he would be heading for defeat. Considering the unspeakable shambles he inherited from George W Bush this is, of course, unfair. But a deal's a deal. The President promised to fix the economy and has yet to deliver. Only Mr Romney's ineptness has kept Mr Obama in the race.

The leaked footage of a candidate dismissing 47% of Americans as panhandlers should have killed Republican chances stone dead. Instead, in a neat piece of symmetry, 47% is exactly the support allocated to each candidate by polling averages. Mr Obama won the third debate, just as he won the second, but it makes no difference. He could still lose to an opponent who relies on magic numbers and the ability to adopt and discard policies on demand.

Many registered voters truly believe such a figure is worth a shot. They do not form part of the so-called conservative base that is fast losing its ability to decide America's elections. Most would define themselves as moderates and independents. Plenty, by definition, are disillusioned former supporters of the Obama who offered hope and change. The polls report, nevertheless, that these mainstream citizens are prepared to buy what Mr Romney is selling.

The hard economic facts say such people are preparing to vote against their own best interests. They are ready, after a mere four years, to restore to power the ideologues of the shambolic Bush years. They are content to back a candidate who speaks, first and foremost, for the very rich. And all because Mr Romney has followed the old Richard Nixon dictum: be right-wing when seeking the nomination, conciliatory when seeking the presidency.

So where stands the American mainstream? It lies on the fault-lines of a divided polity, in a nation that seems, increasingly, irreversibly, like two countries. The defection of a relatively tiny group fed up with Mr Obama could put Mr Romney in the White House, but the result will be in no sense decisive. Is it possible even to govern such a nation?

Let's say Mr Obama hangs on to win in that handful of swing states. He could gain an advantage in the electoral college even if he loses the popular vote. But what then? His party will not retake the Congress. The Republicans will not become "bipartisan". They will continue to do what they have done for four years and obstruct the Democrat at every opportunity. Once again, he will be deemed a failure.

You could say he has only himself to blame. Had Mr Obama governed as he promised to govern, you might argue, Mr Romney's challenge would have faded months ago. But that isn't even half the story. The fact so many states are locked up for one candidate or the other is as much a cultural phenomenon as it is a political reality. In America today change happens on the fringes.

It happens there, nevertheless, and the fact could put Mr Romney in the White House. His economic masterplan is this: he means to close "loopholes". That's it. Yet for a few islands of floating voters in a vast, deadlocked country, it's enough.

No doubt those citizens complain Mr Obama failed to keep his word. Perhaps that was always an impossible dream. Perhaps it has become impossible for any president, of any party. If so, even Mr Romney won't talk his way out of the mess.