Ostensibly, Mr Major's trip will be dominated by such issues as Bosnia, Russia and the world economy. In fact it is President Clinton's invitation to Pennsylvania, where Mr Major's grandfather, Abraham Ball, once lived, that has sparked media interest.
While officials have provided sketchy detail of the agenda for bilateral meetings, they are forthcoming about the life of Grandfather Ball, who built blast furnaces for Andrew Carnegie in the late 19th century and raised Mr Major's father in the US. Abraham Ball was a master craftsman who ran at least one business in Pennsylvania after working for Carnegie. (Mr Major's father was born on a trip back to the West Midlands in 1877, but returned with his mother to the States and lived there until his late teens).
The Prime Minister's programme, though still vague, shouts 'photo-opportunity'. Mr Major once devoted a party political broadcast to a sentimental return to his childhood home in Brixton, south London. Now a visit to an ancestral site in the US is on the cards, although it is not clear exactly where he is heading: the records of the steel company for which Mr Ball worked appear to have been destroyed 50 years ago. There is circumstantial evidence placing him at the Edgar Thompson mill at Braddock, but Mr Major is not expected to visit there.
Is Washington going out of its way this time to court a British prime minister, or is this just part of a new glitzy White House act? The idea of the visit to Pennsylvania arose in a casual post-prandial conversation between the two leaders at the G7 meeting in Tokyo last July. But it looks as if Mr Major's new press secretary, Christopher Meyer, a former deputy ambassador to the US, has called in all his favours in Washington to win the Prime Minister top treatment.
President Clinton is extending more than average hospitality. After his heritage visit, Mr Major will make Monday's journey back to Washington in Air Force One, the President's private plane, abandoning a more spartan British aircraft. Then he will stay in the White House, which, British and US diplomats point out, is a privilege enjoyed by no British prime minister since Winston Churchill. No Western leader will have been in such close proximity to Bill, Hillary, daughter Chelsea, and the US's First Cat, Socks.
That, at least, is the plan. These trips do not always turn out as leaders hope. Observers remember Mr Major's visit to Bermuda in 1991, when George Bush sparked headlines by commenting that Mr Major looked exhausted. Such was the anonymity of the relatively new Prime Minister that a US news agency picture of him with President Bush on a golf cart was captioned 'President Bush and a security man'.
And before the British get carried away, they should remember that others, too, get Mr Clinton's red-carpet treatment. The President has already hosted a friendly and informal restaurant dinner with Chancellor Helmut Kohl in Washington. Next month he will be giving a similarly warm welcome to Albert Reynolds of the Irish Republic on St Patrick's Day. Those same US diplomats who highlight the rarity of Mr Major's overnight stay in the White House point out to the Irish that Mr Reynolds will be guest of honour at a state banquet; there have been, they stress, only a couple of those since Mr Clinton arrived in the White House.
Nevertheless, Mr Major may be benefiting from an element of US guilt over Mr Clinton's decision to allow Gerry Adams, the president of Sinn Fein, into the country last month. The scale of the rupture in Anglo-US relations was made clear by the revelation that it was Mr Major, not (as is usual in these cases) the Foreign Secretary, who delivered a fierce reprimand to the US ambassador in London, Ray Seitz, when the visa was granted.
The stresses, however, are not all one way. On the US side there is still anger among some in the administration at the Conservatives' help for the Republicans during the last Presidential election, and reports that Home Office officials scoured files to search for material damaging to Mr Clinton. There is, however, no evidence that Mr Clinton bears a grudge.
More serious are structural changes in a relationship that is clearly of declining importance for the US. The Cold War security dimension is much reduced, with US air bases in Britain being closed down. Conservative ambivalence towards the European Union makes it a rather awkward partner for the US.
Britain does not, according to US diplomatic sources, 'have the same influence in Brussels as it would if it were an unabashed supporter of European union'. The US term for Britain's position is the Yiddish 'kibitzer' - someone who carps from the sidelines. The blunt truth is that, in American eyes, the Netherlands has more influence in Brussels than Britain does.
As far as Nato is concerned, the US would like a strong, effective, cohesive and well- resourced European component of a US-led institution.
Britain refused to back earlier US initiatives on the former Yugoslavia. And it was France's tough stand, which led to the air-strikes ultimatum to the Bosnian Serbs, that struck a chord in Washington and left Britain struggling to keep up.
Despite all these factors, Mr Clinton has various reasons to keep relations with the UK sweet. He wants to nail the claim, made often in the US, that foreign and economic policy is directed more to the East than to Europe. His visit to Nato recently will be followed by a trip to Britain in June, when he may pay a sentimental visit to Oxford, where he was a Rhodes scholar, before sailing from Portsmouth with other world leaders to mark D-Day.
Moreover, the relationship between Britain and the US operates at many levels. Because of UK membership of the UN Security Council, the EU and Nato, diplomatic traffic is incessant. As Anthony Lake, Mr Clinton's national security adviser, said last week, the telephone on his desk is programmed to dial his opposite number in Downing Street, Roderick Lyne, at the touch of a button. Major-Clinton calls are frequent and, say those who see the transcripts, 'very friendly John-Bill interchange'.
From Mr Major's point of view, a foreign-policy success is much needed. According to one senior Tory, 'He needs to come back looking a bigger man than when he went' to steady backbench nerves. But while the potential bonus of this week's trip are great, so are the potential pitfalls. The travelling press corps would seize on any evidence of friction between the leaders or snubs to the Prime Minister.
Ireland may still become an issue to embarrass Mr Major. As the Prime Minister rises to speak on Tuesday to the British/American Chamber of Commerce at the Waldorf Astoria hotel in New York, the irony will be lost on very few. It was from there that Mr Adams launched his propaganda offensive against the British government less than seven weeks ago.
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