In the end it was incompetence that did it. The presidency of Jimmy Carter already had countless problems, but one event came to stand for all the others: Operation Eagle Claw, the aborted attempt to rescue US hostages from the Iranian embassy in April 1980. That fiasco in the Iranian desert, which ended in the death of eight US servicemen and which rescued no one, hardened the view of the American people that the man in the White House was simply not up to the job. Carter was ejected from office a matter of months later.

William Hague's botched mission to rebel-held Libya is more farce than tragedy: unlike the eight Delta Force men who ended up dead in Eagle Claw, the eight-strong British team of SAS soldiers and MI6 officers, choppered in the dead of night into eastern Libya, suffered nothing worse than a spell in temporary detention and a measure of humiliation. There was more of the latter for Hague himself on Monday, as the foreign secretary had to stand at the dispatch box while his opposite number taunted him with quotes from the rebel council in Benghazi, expressing their bemusement at the Brits' "James Bond" antics. No wonder, given that London had already established phone contact with the anti-Gaddafi forces and so could simply have sent its "diplomats" in by regular flight to the local airport – or, easier still, had them make the two-mile journey from HMS Cumberland, which just happened to be docked in Benghazi port.

You almost feel sorry for Hague. The Arab spring is proving rather chilly for him. First came his premature announcement that Gaddafi was en route to Venezuela. Next came his failure to move quickly to get British nationals out of Libya, the government casting around to find an aeroplane until it was eventually reduced to flying Air Iron Maiden – or, as it is officially known, Astraeus, the charter aviation company whose marketing director and chief pilot is Bruce Dickinson, front man for the metal band. Hague, as they say, is not having a good war.

There is a specific point here about the foreign secretary who, despite his ill-starred tenure as party leader, was always highly regarded in Westminster and not only among Conservatives. Fluent and sharp, Hague was blamed by few for the hammering the Tories suffered in 2001, with most concluding that to lead the Tories during the heyday of Tony Blair was a hospital pass that would have felled anyone. But officials in his own department report that Hague is curiously disengaged. That the body is present while the mind seems to be elsewhere.

Some Westminster villagers wonder if the trouble is that he feels excluded from the inner circle, absent as he is from the key Cameron-Osborne 8.30am and 4.30pm meetings at No 10. Others speculate that the turning point was the intensely personal statement Hague gave last September to quash rumours triggered by his sharing a hotel room with a young male aide. At the Tory party conference a few weeks later many remarked that the foreign secretary looked a pale version of his former self. Plenty wonder if he is marking time, eyeing a post-political life writing biographies, giving after-dinner speeches and fulfilling what, I hear, is a long-held dream of cultivating a farm in remotest Montana.

If Hague is hastened towards that early retirement, it will not be a failure to sketch out a foreign policy doctrine that proves his undoing, but rather these doubts over his competence. And this is something that should preoccupy not just the foreign secretary, but the entire government.

One veteran of the Gordon Brown administration remembers with a wince the 2007 fiasco of the missing discs, when the government had to admit that two CDs containing the personal and bank details of almost 25m people had been lost by the taxman. The Tory opposition tormented Brown: "Never mind getting a vision, you should get a grip." In politics, taking an ideological stance will always mean you lose someone. But develop a reputation for incompetence and you lose everybody.

Usually such a problem arises towards the end of a government's life, when ministers are growing tired, when a smell of decay begins to hover. But this government is already developing a competence problem.

The evidence is there in the bonfire David Cameron had to make of his own forestry sell-off policy, in the bungled announcements last summer of which schools would and would not face the axe to their planned buildings programme – a list that had to be issued and then re-issued no fewer than four times – and in the blaming of an economic contraction on the wrong kind of snow. The prime minister, who rightly won plaudits for his graceful apology following the Bloody Sunday inquiry, seems to have developed a taste for saying the hardest word. And "sorry" certainly has its uses. It casts him as a different kind of Tory PM, reasonable and listening where Margaret Thatcher was stubborn and dogmatic. It also wrongfoots the opposition: where do you go once the government has put its hands up?

But apology is a coinage that gets debased through overuse. Do it too often and the public soon comes to believe the serial apologisers are alarmingly accident-prone.

That last problem is particularly pointed for Conservatives. Their small-state ideology rests on an unspoken premise that government should do just the basics and do them well, crafting a lean machine that, undistracted by the busybodying favoured by the centre-left, concentrates on doing less, better. For Tories that core service would always include policing and national security – which is why cutbacks in the former and cock-ups in the latter play so badly.

Voters have long understood that governments cannot do everything with the wave of a wand. Indeed, the limits of elected power are on display every day of the week. In the US it's the sight of President Obama forced to buckle on his promise to end military trials at Guantánamo. In Britain, it's ministers watching lamely as bankers ignore politicians' pleas and pay themselves ever heftier sackfuls of cash. (The beneficiaries of the latest Barclays bonus bonanza include the exquisitely named Rich Ricci, which suggests the bankers' saga is scripted by a combination of Charles Dickens and Viz.)

So the old delusion – that politicians could fix any problem – has long faded. We know they can't do everything. But we do expect a basic level of competence. If they are sending fighting men into a faraway desert, we expect them to know what they're doing. And if they don't, our judgment can be harsh. Just ask Jimmy Carter.