Mr Barroso told The Independent that this week's summit on EU finance is a defining moment for Britain's relationship with the EU and, particularly, its newest member states.
He argued that, while Mr Blair has problems with public opinion on the EU, voters should understand that European spending will be concentrated on policies that the UK supports. He added: "The role of true, leadership is to explain the difficult issues and not to give up in the face of irrational arguments."
Mr Barroso's allies believe that Mr Blair wants to be flexible but is constrained by domestic politics. However the European Commission president says the stakes this week are high, both for Britain and the EU. Another breakdown would paralyse the EU and wreck hopes of a deal on global trade.
Mr Barroso also said that the 10 new member states in the EU resented the budget proposed by Mr Blair, and the budget would not be large enough to allow Bulgaria and Romania to join the EU as planned in 2007. The new nations are desperate for an agreement to free up the flow of EU subsidies.
The Commission president made a coded appeal to Mr Blair to compromise over the British budget rebate, arguing that "everybody has to move".
However he backed Britain's call for a review in 2008-09 of all EU spending which could lead to cuts in farm subsidies before 2013.
Britain has been at loggerheads with the French over the cuts in farm subsidies. According to yesterday's Sunday Times, Charles Crawford, Britain's ambassador to Poland, in an e-mail to colleagues, blamed the Common Agricultural Policy for payments which "bloat" French landowners and "pump up food prices" in Europe, causing poverty in Africa.
Mr Blair's claims to be at the heart of Europe face their ultimate test this week, Mr Barroso argued. He said: "Does Britain want to be seen as a very important, but periphery country, or a power that is really shaping the future of Europe? That's the strategic point and there is a great opportunity here." He argues that the UK agenda for more EU expansion and economic reform and liberalisation cannot be achieved with the niggardly budget proposed by London.
The UK wants to trim €24bn off a deal proposed in June - some €14bn of which would be taken out of regional aid for the new member states. The UK says they will be unable to absorb all this cash.
Pointing to Mr Blair's Hampton Court summit on modernising the EU, he argues: "There is a contradiction between the ... ambition for a modern, open enlarged Europe and the ... means to achieve it." He added: "With that budget we cannot accommodate Bulgaria and Romania. If there is no [EU] financial agreement we will suffer ... because the conditions for a more efficient [trade] round will not be there, Europe will be paralysed. There will be no conditions for ambitious results in terms of trade if we do not get a fair agreement on the financial perspectives."