They may be having some success. Some of the patronising nicknames are already sticking, while the dreary parrot cry, 'Where's the beef?' now accompanies every speech and interview Mr Blair gives. Conventional wisdom can form with alarming speed and be stubbornly difficult to dispel. If the idea enters the collective mind that Tony Blair is no more than a nice young man who talks enthusiastically about the importance of communities, there is a danger that it may lodge there. Unfortunately, there may not be much he can do about it for the moment.
Tomorrow, Mr Blair is expected to publish what supporters are enthusiastically touting as his personal manifesto, a 5,000-word document which will lay down the principles he wishes to bring to the leader's job. As a statement of Mr Blair's philosophy, it will be important and interesting. It will not, however, do much to satisfy the critics who claim to want to know exactly what a Blair government would be like. Nor should it.
The truth is that Mr Blair's position is not quite as strong as it appears at first sight. There is no question that he is going to win the leadership on 21 July at a canter. But he was rather less of a shoo-in a few weeks ago. It was, at least in part, despised newspaper opinion polling that enabled the Blair camp to persuade Robin Cook and, far more crucially, Gordon Brown to pull out of the leadership contest.
The polls did not, however, provide entirely comfortable reading for Mr Blair. They showed that he was the favourite to become leader because he was the candidate most likely to deliver victory over the Tories, but not necessarily the one whom Labour members most approved of. When it comes to what Mr Blair stands for and what the emerging Blair agenda may look like, there is, in the party, a potentially volatile mixture of suspicion and trepidation. In its yearning for power, Labour knows that it needs Blair, but that does not yet mean that he has won its heart. It is worth recalling the battle that John Smith, loved on all sides, had last autumn to persuade the conference to accept even half- hearted constitutional reform. Although Mr Blair will be leader a month from now, he cannot be certain that the party will immediately be ready to do his bidding.
One of the reasons Mr Blair must tread carefully is that he is to some extent, like Mrs Thatcher when she became leader of the Conservatives, an outsider within his own party. The parallels should not be taken too far, but they are instructive. Mrs Thatcher was able to launch her coup against the Tory establishment because its nerve was shattered after the digressions and disasters of the Heath government. Mr Blair is able to launch his because the old establishment of the Labour movement has been shredded of confidence and legitimacy by four successive election defeats and the terminal decline of labourist collectivism.
But while Mrs Thatcher was not the first outsider to become Tory leader, Mr Blair is the first Labour leader not be steeped in the party's culture and traditions. Therein lies his appeal to the wider electorate, but, at least to begin with, it will make his task more difficult.
Two things are clear. First, Mr Blair cannot simply change established party policy on the wing. Second, he has no need to turn a leadership campaign that he is certain to win into the basis of his mandate. As one close colleague put it: 'They all know that they are not going to get John Smith Mark II, but the details will have to come later.'
His priority must be to gain control of the decision- making levers within the party, most of which are pretty wobbly, then change them. The way in which Labour currently forms policy is typically clumsy and bureaucratic. It engages large numbers of party functionaries and union officials who have no particular expertise in a great deal of committee work that eventually requires validation by a conference still dominated by the block vote.
Unless Mr Blair can win himself some freedom from this nightmarish process, he will find it impossible to put together the ideas necessary to form a programme for government. At the last election Labour suffered from a lethal combination of insufficient thought and excessive detail, the best example of which was the ill-conceived tax and spending plans presented in Mr Smith's alternative budget.
But while detailed policy formulation will be vital for the success in office of a Blair government, it is not that which will cause the electoral earthquake required to defeat the Tories. The voters must gain an instinctive understanding of what Mr Blair is about, and recognise the conviction he brings to changing his party and the country.
It is worth looking at the Thatcher example again. In 1979, Mrs Thatcher could not count on the total support of all her senior colleagues for what she wanted to do, and there was precious little indication from the Conservative manifesto - even if you read it closely - of what was in store.
Conservative think-tanks had been beavering for several years, but it would be easy to exaggerate their influence in the party, let alone in the world outside.
What made the difference was the determination and moral fervour Mrs Thatcher brought to her work. The electorate could sense that she knew what she wanted to do and that nothing would deflect her. Compared with the tiredness of the then Labour government and the cynicism of some of her colleagues, Mrs Thatcher, at least for a moment, offered the possibility of something better and fresher.
Not many people would find similarities between Margaret Thatcher and Tony Blair. But Mrs Thatcher was engaged upon a project of transformation, and so is Mr Blair. He does not share her ideological rigidity, but he does have her certainty and her toughness.
It may be a little while before its final shape becomes clear, but nobody should doubt that the Blair project is a formidable enterprise, which will take some stopping. The Tory tabloids will discover that Mr Blair is not quite as nice as he looks.