Gordon Brown is turning into a political equivalent of Schrödinger's cat who was - in the Austrian physicist's thought experiment - declared to be simultaneously dead and alive. Edwin Schrodinger proposed enclosing the animal in a steel container with a vat of poison that would be released at random. It was, he argued, impossible to know without opening the box whether the cat had been killed, so it could, therefore, be said to be between life and death.

The Prime Minister is in a similar position. On the face of it he is in political good health - he munches his way through summit dinners and declares war on knife crime. And yet, in Westminster, the perception is taking hold that he is a dead man walking. The only topic of conversation among Labour MPs is whether their leader can survive, and who might replace him.

Formerly loyal members of the Cabinet now say that they “don't know” whether Mr Brown will still be there at the next general election. The plotters claim that he will be out by Christmas. There are endless discussions about how the Prime Minister could be dispatched, ranging from the men in grey suits to the men in white coats. The latest plan I heard was for Neil Kinnock to persuade him to stand down on the ground that not all politicians are suited to being leader.

At one level it is all ridiculously over the top. But if the speculation goes on for much longer it will be difficult for the party to pull back, so damaged will be the political authority of the man in charge. Every event, however minor, now plays into the leadership question. As one Downing Street adviser put it: “The voters and the media are like stroppy teenagers convinced that everything their parents do is wrong. Even if Gordon did something right nobody would believe it.”

The by-election in Glasgow East has been described as the crucial tipping point. I don't think it is. It would be bad if Labour lost such a safe seat, of course, but it would only confirm what we already know: that the Government is unpopular even in Mr Brown's Scottish backyard. In any case the party may yet win.

Labour's national policy forum, which starts in Warwick next Friday, could be more dangerous for the Prime Minister in the end. This is the meeting at which ministers, MPs and activists are supposed to agree policy priorities for the next four years. It should set the agenda for the party conference in the autumn and decide the themes of the manifesto for the next general election. And yet there seems to be a vacuum where Mr Brown's vision should be.

The documents circulated in advance of the meeting are a mixture of platitudes and clichés. The transport paper concludes, for example, that “meeting Britain's future transport needs is a complex challenge” - it is unclear whether road pricing should be introduced.

Labour wants to “improve the supply of affordable housing” but there are no suggestions about how this should be done. “By encouraging rights and responsibilities,” the crime paper says, “we can create a better society.” The only new policy that I could spot in more than a hundred pages was the suggestion that all schools should be sent a copy of Al Gore's film on the environment, An Inconvenient Truth.

Downing Street would no doubt argue that the policy forum is no place for making real plans - although if it is not, what is the point of having it at all? But if there is no clear sense of direction from the top other people will try to seize the steering wheel.

The trade unions and pressure groups have tabled more than 2,000 amendments to the policy documents, on everything from flexible working to council housing. The danger for Mr Brown is that the story of the next few months will be the resurgence of the Left rather than his own policy plans. “No 10 has produced a bland blank canvas and the unions are trying to paint their colours on to it,” one ministerial aide said. “For Gordon it's all about party management. There's no exciting forward-looking plan."

This is where the Prime Minister is vulnerable. Mr Brown has a habit of growling, after a David Cameron speech: “But where's the policy?” Now ministers are asking the same question of him. “We all thought Gordon was a brilliant policy guru, fizzing with ideas,” one Cabinet member told me, “but it turns out he isn't at all.”

The Government is pressing ahead with building nuclear power stations, Lords reform, city academies and welfare changes - but these are left over from the Blair years rather than being distinctive Brownite proposals. Even the plan to lock up terrorist suspects without trial for 42 days is a hangover.

The new regime seems confused about where it is going. This week's proposal to force people caught carrying knives to visit hospitals was an “eye-catching initiative” rather than a considered plan. There is, as one strategist admits, a “macro to micro issue” with some of Mr Brown's ideas - it is all very well calling for a “new deal” on energy at the Jedda oil summit, but most people are more concerned that vehicle excise duty has gone up.

Ministers complain privately that too many bold policies are vetoed by No 10. Even some of Mr Brown's own proposals- for changes to party funding and the voting age for example - have been watered down. MPs and ministers are depressed by the poll ratings, but they are more worried by the impression that their leader does not seem to have a plan to turn things around. “You can have a problem with personality or policy, but the absence of both is pretty dire,” one minister said.

There will be no coup in Warwick but if the No 10 cupboard is as bare as insiders fear, then the period around the party conference will be dangerous for Mr Brown. By then it will be a question of survival for many Labour MPs. “The question,” one said, “is has Gordon run out of steam, or have we all?”

Times Recommends

• Never believe Demjanjuk is a ‘victim’
• A strong City is not just good for Britain
• Class warrior ready for one last battle