The reactor would operate through nuclear fusion, which mirrors the way the sun produces heat and light. This produces vast quantities of energy with minimal waste.
The US Congress is expected to refuse to fund further research into the creation of an International Thermonuclear Experimental Reactor (ITER), jointly developed by scientists from the EU, Japan, Russia, Canada and the US.
If the Americans withdraw funding, there are fears that the body running the project may next month decide to shelve it indefinitely, although $1bn has been spent on research but before foundations have been laid for a trial reactor.
The US stance has been attacked by the European Commission, which has accused Washington of being influenced by the oil lobby.
The Commission "strongly disapproves of the short-sighted approach of US decision makers, who gamble on the pump price of petrol ... and are never pressurised to make long-term energy decisions.
"ITER without the Americans would mean the end of a dream: that of a world united in the desire to redeem the sin of the atomic bomb by taming nuclear energy."
The scientist in charge of a small, model fusion reactor - built independently of the global project, at Abingdon, Oxfordshire - was pessimistic about the future of fusion research. "We've been directed for 20 years towards trying to prove the basic physics needed for ITER," said Dr Paul Thomas. "In a sense we have come to a crisis in our work. A lot of people are feeling very alarmed."
But fusion could fill a potential energy shortage in the next century if the supplies of oil and gas run low, said Derek Robinson, director of the UK Atomic Energy Authority (fusion)."If this [project] does break down, a lot of people in Europe will be disappointed.
"If we wait and see what might happen, we would have nothing in place. You wouldn't be able to pick up the technology and develop it in 10 years. You could be putting your energy strategy at risk."
More than 150 British scientists have worked on the programme, which is co-ordinated by research centres in Germany, Japan and the US.
British nuclear scientists have been pressing the EU to consider funding a scaled-down experimental reactor that would cost $4bn to $5bn to develop, rather than a $8bn to 9bn full-scale prototype, so the programme would survive the loss of US funding.
Fusion is the Holy Grail of the nuclear industry, because, in theory, it creates energy without producing much nuclear waste, so mollifying the environmental critics of nuclear energy.
Its basic principles were developed in the former USSR by Andre Sakharov in the early Fifties, and since then researchers have tried to turn theory into reality. The inter-national reactor programme is the closest scientists have come to realising their dream of producing a prototype power station that can pump commercially viable amounts of electricity into national grids.
It would work by heating hydrogen to immensely high temperatures, while it is squeezed inside a steel reactor by a powerful electromagnetic field.
Once the gas is heated to more than 100 million degrees centigrade, its neutrons fuse, creating a huge energy surge - the same reaction that takes place inside a nuclear bomb.
But instead of being released with massive destruction the reactor would contain the energy and channel it to drive power turbines.
It would also maintain the electromagnetic field, ensuring that the gases inside stayed hot, provoking further reactions and hence more energy bursts, in the same way that the sun continues burning, warming the Earth.
The main advantage over existing fission nuclear power stations is that fusion would not use a highly radioactive nuclear fuel - plutonium - that eventually needs to be disposed of at controversial reprocessing plants, such as Sellafield.
But its main disadvantages are the high cost of developing the technology and the fact that scientists are still decades from building an effective reactor: facts that have led US members of Congress to conclude that research on the project should be mothballed.
The council for the International Thermonuclear Experimental Reactor project ran out of money in June, after its project had completed its first allotted six years of work, much of which was theoretical and preparatory.
It asked its funding governments earlier this year for money to continue its work over the next three years to develop a trial reactor generating 1.5 gigawatts, at a site in Canada, Japan or Italy.
This is the proposition which has run into difficulties on Capitol Hill.Reuse content