Rupert Cornwell: Poor Obama – Hillary Clinton is doing a fine job

One famous face was absent at the State of the Union address to Congress last week – and it wasn't the designated cabinet member who always stays away from the Capitol building in Washington on these occasions, to provide continuity of government in case al-Qa'ida pulls off the big one. The missing person was Hillary Clinton, and the silly chatter predictably started.

Was it a deliberate snub? Had there been a falling out between Barack Obama and the woman he so narrowly defeated for the 2008 Democratic presidential nomination? Or had Hillary suddenly been taken ill? In fact, a glance at the diplomatic calendar would have instantly dispelled such notions. The US Secretary of State was away in London, attending important talks on Yemen and Afghanistan, a rather more productive use of her time than shaking hundreds of hands and applauding dutifully at appropriate moments during her boss's big speech.

Even so, the non-event was revealing. It spoke to Hillary's celebrity and to the political ambitions that some cannot believe she does not still harbour, despite disclaimer after disclaimer. And it also reminded us that right now she is a hardworking, constantly travelling Secretary of State who seems to be doing a pretty good job.

Such judgements must be cautious. US foreign policy is set by the White House, and the most effective secretaries of state are those who combine deal-making savvy with closeness to the president – such as Henry Kissinger under Richard Nixon, and James Baker in the administration of his old friend George Bush Snr. In the end, a secretary of state's successes and failures are those of the president.

And Clinton has made her missteps, most notably in the clumsy US efforts to persuade Israel to halt settlement expansion. In an earlier era, the State Department might also have paid a price for the translating gaffe after Obama announced his intention to "reset" relations with Moscow. She presented her Russian opposite number, Sergei Lavrov, with a red button inscribed with the word "peregruzka", which was thought to mean "reset". In fact it means "overload" – not quite what was intended. The important thing, however, was that both of them had a good laugh, a sign of how the Obama/Clinton team is improving America's image abroad after the devastation wrought by George Bush Jnr – and of her own awareness of her star power as a tool of public diplomacy.

So Hillary is putting her own imprint on US foreign policy. She constantly emphasises "smart power", which relies less on military might and more on diplomacy. She has used her celebrity to focus attention on issues such as womens' rights and the global fight against poverty and hunger. She has launched a four-year review to boost the State Department's resources and staff, and put policy planning on a longer-term basis. And, contrary to many predictions, her husband, Bill, has not been an embarrassment.

She has worked smoothly with the big-name envoys appointed in key policy areas, including Richard Holbrooke for Afghanistan/Pakistan and George Mitchell for the Middle East. When she was first appointed, and took some time out to study her new brief, there was talk of Clinton's voice being drowned by a clash of other mighty egos. But no longer.

"Hillary and the envoys have shown loyalty, consistency and cohesion, and the structure has worked," one senior ambassador in Washington noted last week. What hasn't worked (at least not yet), are the policies, as the overlapping, seemingly intractable crises in Iran, the Middle East and Afghanistan attest. For that reason above all, a firm verdict on her performance must wait.

But Hillary must be doing something right. Polls consistently show her to be the most popular member of the government. She is lucky that her job keeps her away from America's dysfunctional domestic political system and the deeply unpopular Congress in which she used to serve.

Even so, Obama right now would die for her 65 or 70 per cent approval rating. From there, in today's febrile political climate, it is but a small step to speculation about a new Hillary bid for the White House in 2012.

Now, politics is a funny old business, but that notion seems especially far-fetched. In a public television interview last week, she couldn't have been clearer, declaring she was "absolutely not interested" in running again for public office. Yes, the Clinton network still has the muscle to mount a campaign if it wants, against the sitting president whose fortunes are in serious decline. But all precedent argues against such a move.

Every time an incumbent faces a serious primary challenge (see Ronald Reagan against Gerald Ford in 1976, Ted Kennedy against Jimmy Carter in 1980, Pat Buchanan against George Bush Snr in 1992), the outcome is the same. The challenger is defeated, but his party loses the White House in the subsequent presidential election. That cannot be what Hillary Clinton sees as the last chapter in her political career.

That last chapter has probably begun. Even if Obama asked her, she told the interviewer, she could not imagine serving eight years at State. The job was simply too exhausting. She spoke fondly of life afterwards, "of reading, writing, maybe teaching". And being a successful one-term Secretary of State is surely preferable to no presidential term at all.