Such are the stakes - one senior Western diplomat suggested that how Mr Clinton fares will prove 'crucial to Europe's future security' - that the rewards for the President, if it goes well, are substantial.
Top of the agenda for Mr Clinton at the Nato summit in Brussels is the US-sponsored plan, Partnership for Peace (already compressed to PFP), which treads a middle line between the appeals of several East European governments for early entry into Nato and Moscow's avowed opposition to such a move.
After talks with Peter Boross, the Hungarian Prime Minister, in Budapest yesterday Madeleine Albright, the US ambassador to the United Nations, said Hungary had decided to 'be among the first to accept the invitation to join the PFP'. Hungary's move came after efforts failed to hammer out a joint position on Nato membership with its other three partners in the Visegrad group - Poland, the Czech Republic and Slovakia. Mr Clinton's hope is that once PFP is adopted in Brussels - almost a foregone conclusion - it will contain just enough to appease the leaders of all four countries by the time he meets them in Prague in mid-week.
The PFP plan has infuriated US critics, who believe the President has been blinded by an exaggerated concern for the sensibilities of Russia and will thus fail to grasp what they see as a historic opportunity to lock the eastern states into Nato.
Among those distressed is Lawrence Eagleburger, secretary of state at the end of the Bush administration. In an interview last week, he described the plan as 'a not very useful half-way house' and a 'time- buyer'. He said: 'Too much is being made of the fear of isolating Russia. To provide Poland, Hungary and the Czech Republic with some kind of reassurance is at least to take a bite out of the problem. As it is, we're leaving them in a sort of never- never land.'
For months, the administration was divided over the question. Early last autumn, the Secretary of State, Warren Christopher, and the National Security Adviser, Tony Lake, were tending towards offering early sanctuary to the East Europeans. That trend was reversed by one man: Strobe Talbott, until now US Ambassador-at-Large responsible for Russian policy, and recently nominated by the President to become No 2 in the State Department. Many believe that Mr Talbott, a house-mate of Mr Clinton's at Oxford University and a former Time magazine columnist, is a secretary of state-in-waiting. His conviction that to move hastily to enlarge Nato eastwards would fuel nationalist paranoia in Russia was laid out in a five-page, single- spaced memo typed by himself on his home computer one weekend in early October and delivered to Mr Christopher. The missive apparently hit its target: within days, Mr Christopher and Mr Lake were warning the allies against alienating Moscow. The President also took his old chum's counsel.
Mr Eagleburger believes that the plan and the way it was arrived at also betray a failure by the Clinton administration to cast its foreign policy goals within a wider and more long- term vision.
'You can't go on for ever making up your mind on what your policy is going to be at a summit, two, three, even six weeks in advance - unless what you want is foreign policy by ad hocism,' he said. 'What we need is a picture of the US conception of what its relationship with Europe is going to be over the next decade or two, and why.'
Defenders of the approach - which still goes almost too far for some of the European allies, notably Britain - include the renowned presidential historian Michael Beschloss. 'It is the right course,' he said. 'It does not close the door to full membership later. The tectonic plates are moving in Moscow right now, and I think it is just exactly the wrong moment to give enormous ammunition to the hard-liners.'
On Russia itself, Mr Clinton has no new money to offer, but he is expected to urge President Boris Yeltsin not to waiver in imposing economic reform in the wake of the nationalists' electoral success.
That position, too, was born out of some confusion. Shortly before Christmas, Mr Talbott was widely quoted as advocating not 'shock therapy' for Russia, but 'less shock, more therapy'. The comments were speedily contradicted - not least by the US Treasury, which considered that they might be seen as an invitation to Mr Yeltsin to ease up.