The joke worked, but one reason why it went down well was because it contained more than a grain of truth. With a cabinet reshuffle due during the next three months, the most common speculation in Westminster concerns the cabinet prospects of Mr Blair's most controversial ally. On one day last month three newspapers speculated about three different jobs. If nothing else, this underlines the fact that the future of the Minister without Portfolio presents the Prime Minister with his most acute man- management problem so far.
In less than 10 months of government Mr Mandelson has never strayed from the public eye. So high is his profile that there are at least two Mandelson biographies in preparation, unusual to say the least, for a minister still outside the Cabinet. (Both are by colleagues of mine, Donald MacIntyre and Paul Routledge.)
While few deny his closeness to the Prime Minister, this has only encouraged vicious private criticism of the man seen as Tony Blair's Svengali. The Conservatives have begun to exploit the relationship, with Francis Maude, spokesman on culture, media and sport, claiming that the Dome's problems are a direct consequence of Mr Mandelson's notoriety. So has government damaged the man once synonymous with Labour's red rose makeover? And, with the reshuffle looming, what is Mr Blair to do about Peter?
THE MINISTER knows that this year could make or break his bid for a place in the Cabinet. To achieve that end he has worked hard, consolidating his reputation as a backroom political operator. He still goes to daily meetings to co-ordinate the Government's message, and has been central to the re-organisation of "the centre" of government, boosting its media awareness via the new strategic communications unit.
Behind the scenes, he sits on no less than 11 cabinet committees or sub- committees, even attending bilateral sessions in Downing Street between departmental ministers and the Prime Minister. Mr Mandelson acts as prosecuting counsel, while Mr Blair often looks on. One minister observed: "At committees, when he speaks, colleagues assume he does so with the authority of the PM."
Formidable though this position may be, it was not what Mr Mandelson had in mind last May. In the run-up to the general election, his allies made it clear that he wanted to run a government department, or part of one, to establish his independent political credentials. Instead, the Prime Minister, who relies on Mr Mandelson for advice, gave him a shadowy role as the number two minister in the Cabinet Office. This presents a political problem for Mr Mandelson because it feeds the suspicion that he owes his job simply to Mr Blair's patronage. One of the themes of the reshuffle speculation is Mr Mandelson's friends saying that "it's time to give Peter a proper job".
Yet he remains boxed in on several fronts, both practical and political. The first is his responsibility for the Dome, something Mr Blair would be reluctant to remove, but which is hardly compatible with most cabinet positions. Then there are his famously bad relationships with key colleagues, notably the Chancellor, Gordon Brown. Neither of the other of the Cabinet's biggest hitters, John Prescott and Robin Cook, are fans, or likely to assist moves to jobs over which they have influence.
Despite his media experience, Mr Mandelson has a tendency to attract publicity of the negative variety, which makes him a high-risk appointment. Given the wrong job, he could become the prime target of Mr Blair's opponents. One friend concedes: "Journalists, particularly interviewers, like to get him, rather like they did Michael Howard. They see him as an expert politician who needs rough treatment."
Another concedes that his TV performances are highly combative and can strike a jarring note: "He believes that when you are communicating with the public you have to have a clear message and you have to repeat it." Although he is a proponent of co-operation between Labour and the Liberal Democrats, and the "third way" in politics, Mr Mandelson comes over as a harsh and unyielding partisan.
Meanwhile, the Labour faithful remain suspicious of a man whose claim to fame is his skill as a fixer. Mr Blair is said to have remarked that his modernisation of Labour will be complete when the party has learned "to love Peter". As one Labour source put it: "If the party was going to embrace Peter it was when he delivered the election result for Tony. In fact, in the National Executive Committee elections, the party kicked him in the balls."
Finally there is the biggest problem of all. As the perfect lightning conductor for Mr Blair, Mr Mandelson is rather useful to the Prime Minister just where he is. So what are the options?
Chancellor of the Duchy of Lancaster. This is the simple option involving a straight promotion in his present department, the Cabinet Office, to a full Cabinet-ranking job.
Pros: The present incumbent, David Clark, is vulnerable and this move would allow Mr Mandelson to complete the strengthening of the centre and stay a strategic adviser to the PM on all subjects. In opposition Mr Mandelson advocated a powerful new department based around 10 Downing Street, and if he were given control of it, this could ultimately make him "the real Deputy Prime Minister".
Cons: Mr Mandelson remains a creature of Mr Blair. And, as one Labour insider says, "as head of a sinister-sounding department, the unpopularity Peter attracts would come closer to the PM. While Gordon Brown may try to emerge as the hero of traditional Labour, Tony would be drawing the poison closer to home."
Secretary of State for Culture, Media and Sport. Mr Mandelson has an interest in the arts and may have his eye on this job, currently occupied by Chris Smith.
Pros: It would allow Mr Mandelson to keep his role in the millennium (although some technical difficulties would have to be overcome).
Cons: It would involve finding another job for Mr Smith and remove Mr Mandelson from a central Whitehall role.
Secretary of State for Social Security. The job may become free. Harriet Harman's poor performance since last May is expected to bring with it a move sideways, and down a bit.
Pros: Would place a Blairite moderniser in charge of a crucial policy area, particularly if Mr Blair calculates that Ms Harman was too close to the Chancellor.
Cons: Mr Mandelson is the embodiment of the divide between old and new Labour. Any social security reforms proposed by him would be treated with huge suspicion by the left.
President of the Board of Trade. Could become free if Margaret Beckett is shuffled to Social Security.
Pros: As an economic ministry, but one less powerful than the Treasury, this is a good department for new cabinet ministers to cut their teeth on.
Cons: It involves much contact with Mr Mandelson's adversary, Mr Brown. The later managed to lever Mr Cook out of the post in opposition, and would not regard Mr Mandelson as the ideal colleague.
Minister for Europe. There has been talk of a new cabinet post for Europe, although Mr Mandelson might still be interested in the job of Minister of State for Europe at the Foreign Office.
Pros: Mr Mandelson is a strong pro-European with excellent contacts in the EU.
Cons: Mr Cook is thought to have blocked the idea of having Mr Mandelson in his department last May and is unlikely to have changed his mind. Nor can he be expected to agree to Europe being syphoned off into a separate cabinet ministry.
Secretary of State for Northern Ireland. Could become free if Mo Mowlam, the present Secretary of State, is promoted to a high-profile mainland job.
Pros: An important job but one which takes the minister out of Labour's cabinet dogfight. Intriguingly, Mr Mandelson is thought to be interested.
Cons: Ms Mowlam may not be moveable this year because of the delicate state of the peace process.
The Nightmare Mandelson Scenario. Because of the unexpected success of some older Labour figures, such as Frank Dobson, Secretary of State for Health, Mr Blair decides on a small reshuffle, and leaves no room in the Cabinet for Mr Mandelson.
Most of these are possible, although the first two remain the likeliest. Mr Blair has probably not made up his mind, and can delay doing so for three months. All of which makes reshuffle speculation so absorbing for political professionals and so entertaining for disinterested spectators.Reuse content