European leaders are gathering in Brussels today for what is likely to be remembered as one of their most significant summits in years.
They are expected to approve a special deal for Britain, in return for its staying as a member of the European Union (EU).
They must also adopt new measures to police the EU's frontiers, now breached from all directions by refugees.
"This is a critical moment," Mr Donald Tusk, president of the European Council, the EU's highest decision-making body, warned summit participants, urging them to cooperate. But the European leaders' willingness to compromise is almost non-existent.
British Prime Minister David Cameron has the most to lose from a failure of this summit. He has staked his political career on securing an agreement on a set of concessions that would allow the British government to ask voters to stay in the EU in a referendum, which looks almost certain to take place in June.
In preliminary discussions, Britain has already been promised a number of significant concessions. Under existing rules, EU citizens are entitled to all the welfare payments available to locals in any European country. But to address British fears that this is resulting in an inflow of "welfare scroungers" who come to Britain just to claim benefits, EU leaders are prepared to grant London the right to limit for a number of years the welfare payments it makes to European migrant labourers.
Britain has also been promised that, despite its refusal to accept the Euro single currency, it will be able to influence future Europe-wide financial decisions; that addresses another long- standing British fear that London, by far Europe's biggest financial centre, could be disadvantaged by future European legislation.
The snag for Mr Cameron is that notwithstanding intense behind-the-scenes negotiations, there is no guarantee that all EU leaders would sign up to the compromises being touted.
East European leaders, whose citizens are most likely to be affected by restrictions on welfare payments, want a reassurance that the concessions offered to Britain would not be extended to other EU member-states.
"The European Union needs the United Kingdom and the United Kingdom needs the European Union," said Romanian President Klaus Iohannis, whose country has an estimated 250,000 workers in Britain, "but any deal has to be convergent with the interests of Romania."
There is also concern that the European Parliament might refuse to ratify any deal. MPs are angry that they have not been consulted, and will be spoiling for a fight when Britain asks the European Parliament to approve any deal which emerges.
"I do like the idea of myself being a monkey with a gun," Professor Gyorgy Schopflin, a distinguished academic who is now a European MP for Hungary, jokingly told the British media.
And then there is France, which strenuously objects to any special concessions to London's financial centre. Mr Emmanuel Macron, French Economy Minister, could not resist the temptation of goading Britain this week by promising to "roll out the red carpet" to London bankers who might wish to relocate to Paris should Britain leave the EU.
An equally massive diplomatic tussle is expected over immigration controls. German Chancellor Angela Merkel wants to keep the internal borders between EU member-states open, and argues instead that EU states should share the incoming migrants; at the moment, Germany is the destination for more than 80 per cent of the 4,000-odd asylum-seekers who enter the EU daily.
But the East Europeans, who fear a repeat of last year's chaotic scenes as one million migrants landed in the EU, want border controls imposed around Greece, the country through which most asylum-seekers come.
A possible compromise may be feasible, but all that would do is to keep matters as they are, just as the weather gets warmer in Europe and another wave of migrants is in the offing.
Unsurprisingly, therefore, Mr Tusk is already touting the possibility of yet another emergency summit next month.