Cabinet reshuffles, however tricky, are supposed to be symbolic moments.

In the ideal world of the spin doctors these arcane affairs are meant to demonstrate that a Prime Minister is still in command, still full of vigour, purpose and ideas. The small problem is, there is no such thing as an ideal world.

David Cameron, pen poised over a list of colleagues as autumn approaches, might be about to discover what the truism implies. He intends to do more, we are informed, than just "tinker" with the allocation of jobs for the boys and girls. He means to make another of those famous big pictures. In reality, his Coalition is a mismatched jigsaw puzzle.

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Too many of the pieces in the frame will never fit; too many can never be moved; and too many would never be missed if they simply disappeared without trace. Certain individuals occupy more than one of these categories. One way or another, this is not the sort of symbolism Mr Cameron needs.

The first question to be asked of any reshuffle is a simple one: why? After all, the Minister who is about to be sacked was once proposed as the ideal candidate for the job. So who made the wrong decision? Only the occupant of Number 10 can answer that question.

This was supposed to be a government of all the (non-Labour) talents. It was supposed to work in harmony for the greater good. It was promised, above all, as the Cabinet that would set the economy back on its feet. Things haven't worked out that way. Where failure is concerned, they are truly all in this together. Now Mr Cameron has to attempt to make do and mend.

The second question to be asked when the music stops and someone is short of a Cabinet seat has to do with duress. Has the Prime Minister made his choices freely, or has he been pushed into a corner? Can he pick the best people for the tasks at hand, or are there other, less worthy considerations involved?

For now, Mr Cameron is stuck with the LibDems and must consult with Nick Clegg on the disposition of those forces, such as they are. But with both Chris Huhne and David Laws having made their excuses and resigned, the junior partners have few plausible substitutes waiting on the bench. The Prime Minister must accept what is offered.

Besides, Mr Cameron could not attempt to move Danny Alexander from the Treasury, or Vince Cable from business, without an almighty row. Significant parts of the Cabinet are, if you like, pre-selected. Despite any claims to the contrary, Number 10 can only tinker. That's hardly likely to stir the voters.

Then there are the Tory prospects, and few enough of them. How do you promote likely candidates when fully 90 of your backbenchers have just staged a serious rebellion over Lords reform, one in which they made their disdain for the leadership clear? How do you select from a crew of eurosceptic troublemakers contemptuous of your LibDem partners and somehow maintain the semblance of a partnership?

Mr Cameron could still make a grand gesture. Tim Yeo, the green-minded Tory veteran, has just invited his leader to decide whether he is a man or a mouse amid the dithering over the third Heathrow runway. The simple-sounding insult has several nuances. It asks whether Mr Cameron is capable of boldness, and whether he knows how to be decisive. In the context of a reshuffle, it asks whether Mr Cameron is ruthless enough for the job.

The charge he was faced, time and again, is that he runs his government as a posh boys' club. Not only are the club's members out of touch they are, in the shape of George Osborne, the Chancellor, self-evidently bad at their jobs. The debacle of the last Budget was proof enough of that. So would Dave dump George to eradicate a slur and rescue economic policy?

Plenty of Tories have begun to mutter that Mr Osborne has to go. A poll this week in one of the London papers showed significant support even among those who voted Tory at the last election for a reshuffle that would place Mr Osborne in alternative employment. The Treasury is reduced to boasting, after all, that revised GDP figures showing a merely catastrophic 0.5% contraction are "better than expected". Mr Cameron will stand or fall with this Chancellor. So will he act?

Not a chance. In this lies the truth of any reshuffle. Mr Cameron has endorsed Mr Osborne's ham-fisted strategy at every turn. If he demotes the Chancellor now, he will simply redirect criticism to his own door. There is no indication, in any case, that some other member of the prime ministerial cabal – William Hague is mentioned – would recant from the Osborne doctrine. To repeat: they are all in this together.

Mr Cameron, they say, is loyal. In a Prime Minister, especially a Prime Minister with few enough options, loyalty can look very like weakness. This one cannot imagine life without Mr Osborne. He continues to tolerate Michael Gove, preferring to hear bluster rather than view the evidence of carnage in England's education system. Theresa May's adventures at the Home Office are meanwhile beyond a joke. Yet such individuals seem to make this Prime Minister feel secure.

The real world must seem strange when you are inside the club. Mr Cameron, lost to reality, appears not to realise that those he has asked to provide solutions amid a crisis are in fact the source of his problems. His chances of re- election, though diminishing fast, depend on Mr Osborne's ability to conjure economic improvement. Yet what are the signs? The budget was inept and irrelevant. The Chancellor can sleep easy, nevertheless.

This is truly symbolic, of course. It shows, first, that the Coalition has failed, even on its own terms. The business of government has become shambolic. Worse, being in government matters more to Mr Cameron and his coterie than governing. Pals come first and last. So the reshuffle, like the political skills of those involved, will be a trivial affair.