But that isn't what "Clintonise" means, of course: the question is whether Mr Prescott and colleagues are willing to see Labour become the rightwards- moving populist party that the US President is making the Democrats.
It is a fair bet that few Blairites understand the significance of Clinton's signing the Republicans' welfare reform Bill. Here is a measure which, among other things, takes a great bite out of the heart of the argument advanced in Mrs Clinton's sticky book about protecting children better. More importantly, by returning substantive social policy to the States, it will widen American inequality by miles. It will also win Clinton votes.
Anglo-American comparisons offer all sorts of pitfalls. Most British people think they know the United States, when - thanks to television - they know far more about the organisation of the New York police department than that of the House of Representatives. Cultural differences between the two countries mean that, for example, the "demon eyes" advertisement would be absolutely impossible in an America where Satan's powers are a literal daily belief for millions.
Cosying-up between presidents and prime ministers is a recent and superficial phenomenon. It is difficult to imagine Palmerston tapping his feet while Abe Lincoln played him a selection of pioneer favourites on the harmonium. The famed passion of Ronnie and Maggie led to little of political substance. By contrast, Tony and Bill do have relative youth and a certain political style in common.
So lessons there are. What the President principally has to teach his younger Labour admirer is the art of survival. The past four years are, if nothing else, a tribute to Clinton's resilience. After the great early debacles, such as the failure of healthcare reform, he has been reborn. Whitewater still hangs heavy; some Republicans still hope that the special prosecutor will be their election saviour. But the lesson here from Clinton has to do with staffing. Get rid of duffers and embarrassments. The quality and experience of the inner circle is increasingly important in our quasi- presidential set-up. The top man vitally needs experience at his elbow; a crux role is that of chief of staff, which in British terms means someone an incoming prime minister can carry with him into Number 10 with the savvy to manage not only the official machine and the party, but also the prime minister's weaknesses.
What Clinton has done since the Democrats' staggering losses in the congressional elections two years ago amounts to resurrection. He has been helped, to be sure, by Republican overreach. Newt Gingrich, Republican Speaker, simply failed to deliver his radical anti-statist "contract with America". Clinton has opportunistically preyed on the fears of pensioners and other groups liable to vote Republican but which suck on the teat of state support with Democratic vigour.
Clinton's course has been unmistakably rightward, as measured by reduced social commitments and the promise of fiscal responsibility - the word "social" does not in the US encompass crime and punishment, including the latest moves to criminalise aspects of tobacco sale and consumption. He had to live with a Republican House and Senate, to be sure, but the cleverness of Clinton has been to dress up his repositioning in the clothes of family and children, which gives him a rhetorical lock on the future, despite the substantial reduction in child support in the latest welfare reform.
Analogies with Blair and Labour are limited by history. Labour has always been a statist party. Prior to the New Deal, the Democrats were the party of strictly limited and local government. President Clinton, moreover, has ways of appealing to outcasts from the latter-day Democratic Party. He comes from a southern state and, while sincere and courageous in his support for gun control, will probably during the election do some stunt reminiscent of his rushing back to Arkansas during the 1992 campaign to oversee the despatch of a condemned man. Tony Blair seems unlikely to win the British election by brandishing a length of hemp.
So, Bill Clinton arrives in Chicago today bearing - by implication - two thoughts for Blair's consideration. One is about ruthlessness - which cuts staff and policy commitments when they fail, regardless of loyalties or history. It is a lesson that Blair needs to learn.
The second lesson is that the attempt - accepted as readily on the left as the right in Britain a decade ago - to define political identity in terms of attitudes towards the state and its powers is over. No useful purpose is served by trying to make consistent the essential incoherence of government here as well as there over the limits of state intervention - the Tories have indeed brilliantly succeeded in their confusion. Clinton reinforces this message. On the powers of government, he is supremely eclectic. His measures on tobacco, brutally interventionist as they are, will win party plaudits and electoral approval. They are Big Government in action. Meanwhile, he wows Wall Street with a tax-cutting plan shamelessly devised to upstage the Republicans. This is Lean and Limited Government. All in all, this is not liberalism or collectivism; it is populism. The formula may work for the President this autumn. It cannot, however, be an option for Tony Blair. He should listen to his deputy's account of Chicago. You can't Clintonise British politics and Labour should not even try.