In the notorious US presidential election of 2000, with its “hanging chads” and the interminable recount of votes in Florida, George W Bush beat Al Gore by a whisker, to the chagrin of Britain’s New Labour government. It seemed baffling that, after years of economic prosperity under Bill Clinton, an incumbent vice-president could have let himself be beaten by a word-mangling Texas governor.

For many observers, including myself, there was a simple answer — Clinton, or rather his absence. He had left office on a wave of popularity: had the constitution allowed it, Clinton would have won a third term in office. But Gore, for personal reasons of rivalry and resentment, would not let Clinton campaign on his behalf, thus turning his back on the most accomplished politician of his age.

One of the reasons I think President Obama will win a second term in office — just — is that he is not making Gore’s mistake. Clinton is still the master of the political game. Compare Obama’s limp performance in the first debate with Clinton’s brilliant, mocking dissection of Mitt Romney’s performance. The Democrats can thank their lucky stars that Obama is not too proud to have Bill campaigning on his behalf.

Reporting of the presidential campaign is a bit like high-grade soap opera. For weeks the narrative was all about Obama pulling away in the polls. Then along comes the first televised debate, in which both candidates defy expectations, and the narrative turns on its head. Suddenly, it is crisis in the Obama camp, with fresh wind in Romney’s sails.

There is nothing like a new angle to get journalists’ adrenaline pumping. It also encourages exaggeration. True, the numbers have moved quite sharply in Romney’s favour. He has pulled ahead in most national polls, while in the so-called battleground states, where the race will be won or lost, the gap is tightening, even if Obama retains the advantage in most of them. The election is not a direct plebiscite. People vote state by state, with the winning candidate receiving each state’s allocation of “electors” in a college of 538 members. To become president you must have at least 270 electors in the bag. Obama is still much closer to that number than Romney.

But that is just today’s snapshot. There are more than three weeks for the narrative to change. I remember George W’s campaign people telling me that over the final weekend in 2000, just 72 hours before polling day, they had decided Bush could take his foot off the pedal a little and have some down time. That was a mistake that almost cost him the race.

There are potential game-changers a-plenty between now and election day, among them more debates. The vice-presidential candidates, incumbent Joe Biden and Republican Paul Ryan, were at it last night. Next week there will be another presidential debate. This is an opportunity for President Obama to shine. It will be a “town meeting” in which the two candidates take questions from an audience of undecided voters and debate their answers. Obama was seriously rusty in the first debate, while Romney has done masses of debating in the past year. But the President is good at town meetings, Romney less so.

More importantly, Romney has left himself vulnerable after the first debate. To win the nomination, Romney had to appeal to the party’s core supporters, who are way out on the Right wing, hand in glove with the Tea Party movement. To win the presidency, a candidate must reach out to the centre ground.

In the first debate, Romney started this process of moving back to the middle, glossing over some of his more extreme positions. The Centre-Right is actually his natural political habitat. No wonder, earlier this week, Bill Clinton referred mockingly to “Moderate Mitt … where you been, boy? I missed you!”

Obama should be able to make hay with the gaps between Moderate Mitt and “severely conservative” Mitt, as Romney described himself earlier this year. Throw in the arithmetical inconsistencies of Romney’s budget ideas and a deeply unimpressive speech on foreign policy earlier this week (there will be a third debate just on foreign policy), and Obama has the wherewithal to get the polls moving again in his direction.

But the days are long gone since his rhetoric could inspire millions at home and abroad. The shadow of crushed expectations hangs over his presidency, exacerbated by an anaemic economic recovery. The truth is that Americans have a choice between two vulnerable candidates. The race will go to whichever one is considered to have the fewer flaws.

We in Britain are watching the race closely because it matters to us who wins. Talk of American decline is much exaggerated. The US remains our most important ally and biggest national trading and investment partner.

It is unwise and naive for any British government to express a preference in public for one of the candidates for the good reason that the other may win. Despite New Labour’s profound wish for a Gore victory in 2000, Tony Blair was scrupulously well disciplined in maintaining public neutrality. It is unfortunate that word has got out of Cameron’s apparent preference for Obama, a sentiment shared by the Tories in Birmingham this week, if a straw poll is to be believed.

But they are right. Romney could turn out to be an excellent foreign policy president, yet right now, his foreign policy team is split between neo-con hawks and those of a more pragmatic, “realist” world view, similar to our own. We don’t know which faction will come out on top. In the circumstances, we’re better off with the devil we know — and that’s Obama.

Sir Christopher Meyer was British ambassador to the US, 1997-2003.