French and Dutch voters recently delivered a blow to the EU constitution by soundly rejecting the document in polls.
French President Jacques Chirac and UK Prime Minister Tony Blair have clashed over the EU budget in the lead-up to the summit.
Mr Blair, after a meeting with the French president in Paris on Tuesday, said there is little prospect of their “sharp disagreement” being resolved.
President Chirac, backed by most EU countries, has repeatedly called on Britain to give up its five billion euro (A$7.5b) rebate from its EU budget contributions.
Mr Blair has ruled out such a concession — unless the budget is overhauled to revise costly agricultural subsidies that mainly benefit France.
President Chirac has ruled out any concession on farm payments, which were pegged until 2013, in a deal accepted by Britain.
Luxembourg Prime Minister Jean-Claude Juncker is chairing the two-day meeting, and has made a last-ditch attempt to broker a deal on the 2007-2013 EU budget by making concessions to Britain on its rebate from EU coffers.
He proposed the refund, negotiated by then Prime Minister Margaret Thatcher in 1984, could be scaled down only after 2013 rather than from 2008 as he had earlier suggested.
EU executive president Jose Manuel Barroso earlier said unless the summit resolves the budget problem and finds a way forward on the constitution, Europe will “sink into a permanent crisis and paralysis”.
Mr Juncker has said while member states are close to agreeing on the overall spending level, wide differences over Britain’s rebate and how much other top contributors should pay into EU coffers makes it unlikely a deal will be reached this week.
The German president said he would not sign off his country’s ratification of the treaty until a court rules on whether it fits with the German constitution.
And Italian Prime Minister Silvio Berlusconi also expressed pessimism.
Mr Juncker’s compromise proposes extra cuts for those three countries in their contributions.
The EU budget is worth 106.3 billion euros (A$167.3b) this year.