Prime Minister-in-waiting Gordon Brown has predicted "we'll get what we need" from this week's EU summit.
Gordon Brown will take over as PM on 27 June
But he told GMTV that "if necessary" he would be prepared to hold a referendum on changes to the way the EU is run.
On Monday Tony Blair set out four areas he would not compromise on: the Charter of Fundamental Rights, foreign policy, common law, and tax and benefits.
This removes the need for a referendum, he said. But the Tories say any power transfer must be put to a public vote.
The summit on Thursday and Friday is expected to go to the wire as leaders wrangle over how much of the constitution rejected by voters in France and Holland in 2005 should be revived.
Mr Blair told MPs on Monday an agreement could only be reached on a "conventional amending treaty".
And he set out the four "red lines" which he said would ensure that the treaty did not have the characteristics of a constitution.
Mr Blair and Mr Brown are due to hold pre-summit talks later with French President Nicholas Sarkozy via a video link.
But Mr Blair's hopes of forming an Anglo-French alliance appear to have been dashed, as Mr Sarkozy joined Spain in backing a major expansion of EU powers.
The French and Spanish unveiled a 10 point document on Monday calling for a "single legal personality" for the EU and a legally-binding Charter of Fundamental Rights which could give workers in the UK new rights to strike.
The two countries are also insisting on more majority voting in 51 policy areas including in criminal law and foreign policy.
The Spanish Minister for Europe, Alberto Navarro, told the BBC: "We have full respect for countries like France and the Netherlands who tried to ratify the constitutional treaty and failed, through a popular referendum.
"But it's very difficult and hard to understand why governments who signed this treaty two and a half years ago in Rome in October 2004, suddenly, without having even tried to ratify, have now difficulties."
Britain is now likely to join forces with Poland, which opposes changes to the EU voting system, and the Netherlands, which wants power returned to national governments and opposes a Charter of Fundamental Rights.
Mr Brown will not be attending the summit but he told GMTV he had been kept up to date on progress by Mr Blair.
Asked if he would hold a referendum on the EU when he enters Downing Street, he said "if it were necessary".
But he added: "The question is 'Can we get the best deal for Britain?' and I suspect that the best deal for Britain will be won, where we will get what we want at this summit.
"Of course, it is a matter of negotiation and compromise and other things, but I think we will get what we need."
But the Conservatives said any transfer of power to the EU must be put to a public vote and accused the government of "talking tough prior to a climb down".
David Heathcote-Amory, who was a UK delegate to the body which drew up the original constitution, told BBC Radio 4's World at One programme: "We shouldn't have been in these talks at all."
He said the "secrecy" surrounding the treaty was "depressing".
"The government are now going into talks and we now hear they have got these alarming difficulties, they haven't told Parliament about them, the public haven't been told," he said.
"The British position is really unknown."
Europe Minister Geoff Hoon rejected the accusation, saying there was a full Parliamentary debate on Wednesday on the European Council meeting.
Asked if he was going to the EU summit, he told the BBC: "That's still to be decided, normally speaking the prime minister and the foreign secretary go and I see no particular reason to change that.
"If I can be of assistance.. to assist the process of reaching agreement then I will be delighted to be there."