Mr Major's programme, including a folksy and much trailed joint visit with the President to Pittsburgh, where the Prime Minister's grandfather built blast furnaces, has been designed to dispel the lingering belief that differences over Bosnia, Northern Ireland and the Tories' help for George Bush's presidential campaign, have cast a dark shadow over his relationship with Mr Clinton.
Mr Major has been afforded ample time to talk to the President, about Bosnia and the prospects of extending the Sarajevo ultimatum to other parts of the war zone, the dimming prospects for early peace in Northern Ireland, world trade and economics, Iraq-Iran and, probably, in the wake of the Hebron massacre, the Middle East.
After visiting an urban renewal project and what - if anything - can be found of the steelmaking Pittsburgh which Mr Major's father and grandfather knew, they will dine in the city before flying to Washington in Air Force One.
Senior officials in both governments acknowledge that both the differences over military intervention on Bosnia - in which Britain only backed the air strikes after the French abandoned their opposition to the US on the issue - and President Clinton's decision to admit Gerry Adams, president of Sinn Fein, have imposed strains on Anglo-US relations.
But officials in both governments are equally adamant that the personal relationship between the two men is warm. The British decision that backing for the Bosnia ultimatum was essential in the interests of what Douglas Hurd, the Foreign Secretary, called the 'strength and solidarity' of Nato, followed what US sources say followed two or three 'lengthy and productive' telephone calls between Mr Major and Mr Clinton.
British and US sources also argue that the meeting is coming at a 'propitious moment' - after the 'partnership for peace' agreement concluded by Nato in January and the successful conclusion of the Uraguay trade round. The success - so far - of the Sarajevo ultimatum and indications that the US administration is unlikely to admit Gerry Adams again unless the IRA renounces violence have also helped to smooth the run-up to the talks. British officials say that other disagreements - for example over the US invasion of Grenada in 1983 - were if anything more traumatic.
This morning, Mr Major will breakfast at the residence of the ambassador, Sir Robin Renwick, with a clutch of President Clinton's most senior foreign policy advisers, including Warren Christopher, the Secretary of State, Assistant Secretary Strobe Talbott, the architect of the President's security policy towards Russia, and Jim Woolsey, Director of the Central Intelligence Agency. He will then meet Al Gore, the Vice President, before seeing senior Congressional Leaders on Capitol Hill.
And at an economics-centred lunch Mr Major, whose party will include Sarah Hogg, the head of his policy unit and Mr Major's main liaison official with the White House during the Gatt talks, will meet Lloyd Bentsen, the Treasury Secretary, Mickey Kantor, the US's senior Gatt negotiator and Alan Greenspan, chairman of the Federal Reserve Bank.
The 'special relationship' is still valuable to both America and Britain, despite recent strains, a Centre for Policy Studies pamphlet argues today. Anthony Hartley says that on issues like terrorism and trade, Britain is closer to the US than to other countries.