By Paul Reynolds
BBC News Online world affairs correspondent
Disappointment will give way to dismay in the European political establishment if the apathy of the European elections is followed by a failure to agree a European constitution.
Talks may go to the wire: Bertie Ahern and Jacques Chirac
The 25 EU leaders meet in Brussels on Thursday and Friday for what should be the decisive meeting to resolve the outstanding constitutional issues.
It is likely that in true European style, the talks will go down to the wire.
A lot rests on the noted negotiating skills of the Irish Prime Minister Bertie Ahern. Ireland currently holds the EU presidency and will guide the talks.
"I think the chances of success are 50-50," said Heather Grabbe of the Centre for European Reform in London. "They have a lot to sort out. It is touch and go."
Other observers are more optimistic.
February 2002: Convention starts work
June 2003: Draft submitted to EU Thessaloniki summit
Autumn 2003: Intergovernmental conference debates constitution
December 2003: Brussels summit fails to agree final text
May 2004: EU enlarges to 25
"I believe they will agree," said John Palmer, Political Director of the European Policy Centre in Brussels. "There is another reason to hope for success this time.
"A failure would deal a further unwanted blow to their collective prestige and credibility after the European elections.
"The bigger problem will be with the ratification of the treaty, especially in Britain."
These are the most difficult issues:
Voting rights: Last time round in December, Poland and Spain blocked agreement because they would have lost out through changes in how many votes each country gets. The Irish presidency is now proposing that for a vote to be passed, it would have to have the support of 55% of member states representing 65% of the EU population.
This is a slight improvement for middle-sized states from the 50%-60% double majority proposed before.
However, Poland's Prime Minister-designate Marek Belka is facing a vote of confidence in parliament on 24 June. So he will not want to give much ground.
Spain, with its change of government since the Madrid bombs, seems more flexible but an agreement is not assured.
Size of the Commission: Smaller states want a commissioner for every member state, not the reduced commission proposed. The compromise suggested is to keep one for each until 2014, then cut back, a classic Euro fudge.
Charter of Fundamental Rights: The argument here concerns whether this applies to all laws or just to EU ones. The British insist on the latter. Otherwise, they feel, domestic industrial law will be undermined.
Stability Pact: Germany and the Netherlands are arguing about whether finance ministers must strictly follow the rules on budget deficits.
God: Will God and/or Christianity be mentioned in the treaty's preamble? Poland and Italy want a reference. France, with it public secular traditions, does not.
The Irish have proposed dropping a quote about democracy from the ancient Greek writer Thucydides which has brought objections from Greece and Cyprus.
Qualified Majority Voting (QMV): Otherwise known as the British "red lines." The UK is insisting that in tax, foreign affairs, defence, social security, treaty change, criminal law and financing the Union, all states must agree.
British officials say that problems remain in several areas despite compromises proposed by the Irish presidency.
The problem areas in QMV are:
Tax: The proposal for QMV only affects administrative co-operation and tax evasion. Even this goes too far for London.
Social security: The draft text wants QMV on the payment of benefits, which Britain says would clash with its tax credit system.
Criminal Law: Britain is opposed to a European Prosecutor.
The Irish have proposed that if in future there is no agreement on bringing aspects of law closer together, those countries who want to go ahead by themselves could do so after a delay. This has the makings of a compromise.
"There can be no chink in the armour on any of these issues," said a Foreign Office diplomat in London.
With a referendum due in increasingly eurosceptic Britain, nobody doubts the government's resolve.
"Tony Blair will be even more hawkish," said Heather Grabbe, of the Centre for European Reform. "He is concerned at how the public will react to the constitution.
"This will strengthen his argument that his red lines must be respected. But others will be just as determined. Marek Belka is quite ready walk out without a deal on voting rights."
And if there is no agreement?
"They have the nuclear option," she said, "It is for a period of reflection during which
some will argue for the whole thing to be rethought. It is, though, very much Plan B."