For a short while it looked as if the Americans might pull it off with their compromise proposal to put a cap on the use of trees and farmland as "carbon sinks" for greenhouse gas emissions - until the EU's number-crunchers did their sums.
Frank Loy, the old Ivy League lawyer who heads the US delegation here, had stolen the limelight on Monday night with what appeared to be a major concession. All the Americans needed was to persuade the EU to go along with it and then a deal could be done.
By lunchtime yesterday it had all begun to fall apart when Dominique Voynet, the French Environment Minister, who was even wearing a Friends of the Earth "Face Up To Climate Change" brooch, took the stage to rubbish the US proposal.
Speaking on behalf of the EU, she laid it on the line that what the Americans were offering on "sinks" was simply unacceptable because it could lead to a 9 per cent increase in US greenhouse gas emissions rather than a 7 per cent decrease.
In other words, by claiming credits for maintaining its existing forests and farmland - an essential addition to swing the votes of senators from midwest agricultural states - the US would not have to do anything to cut its prodigious emissions.
Her blunt statement that the EU was not even prepared to debate the issue threw the cat among the pigeons and simultaneously scotched speculation that Europe was about to cave in; it also made the prospects of a deal here less likely.
With only three days to go, it is hard to see how the gap can be bridged between the EU, which is anxious to meet its commitments under the Kyoto Protocol, and the US, Canada, Japan and Australia, which want to implement it as painlessly as possible.
The bottom line for the Americans, as Mr Loy made clear, is that any deal cut in The Hague must be cost-effective, with no restrictions on the use of flexibility mechanisms, so that the protocol can be ratified by the US Senate.
Two years ago the Senate voted by 95 to zero against any move to implement the Kyoto target of cutting greenhouse gas emissions by 7 per cent, at least until major developing countries such as China and India also agreed to cut their emissions.
The same message has been spelt out here this week by eight sceptical members of the US Congress. They were immediately branded as the Gang of Eight by US environmental groups because of their black voting record on green issues.
While their press conference was in progress, they suffered the indignity of being presented with individually named Barbie dolls, each with its head stuck in the sand, to symbolise their refusal to face up to the grim reality of climate change.
The truth is that US politicians are not prepared to cut greenhouse gas emissions by 7 per cent if this would precipitate a downturn in economic growth. However, as Mr Loy pointed out, although the US economy has grown by more than 4 per cent a year over the past two years, greenhouse gas emissions have gone up by only 1 per cent. To that extent the US is managing to "decouple" pollution and growth.
The problem facing the US delegation is whether any agreement reached here will "play in Peoria", in Richard Nixon's phrase; a reference to the small town in Illinois which he always regarded as a bellwether of Middle America.
Even though 1,500 people in major US cities are dying every year from heatstroke, and this fatality rate is expected to double by 2020, Americans have still not made the link between their annual heatwaves and global climate change.
But public opinion in the US is changing fast, according to Tony Juniper, campaign director with Friends of the Earth. "As weather-related disasters become part and parcel of everyday life, people will be demanding action from the politicians," he said.
Sweden's Environment Minister, Kjell Larsson, agreed. He said yesterday that he would be prepared to place bets with anyone that, in five years, "people will be saying `Why didn't you do more?' in Kyoto and The Hague to deal with it".
He also put the US offer in perspective by saying that it would allow Sweden and Finland, Europe's most forested countries, to increase their greenhouse-gas emissions by up to 40 per cent "if we were looking at this from a narrow national interest". Instead, both countries have rowed in behind the common EU effort to reduce emissions by 8 per cent on 1990 levels by 2010. And in Sweden's case, as he proudly pointed out, there had been a zero increase over the past decade.
Jim Currie, the Scottish director-general of the European Commission's environment division, said there were huge opportunities for US business in implementing Kyoto, citing the EU's deal with motor manufacturers to cut carbon emissions from cars.
He also suggested that the Global Climate Coalition, the most virulent opponent of doing anything to halt climate change, had become something of a toothless tiger following the withdrawal from its ranks of all the oil companies apart from Exxon.
According to Mr Loy, President Clinton is also concerned about climate change. However, this concern may not translate into authorising the US delegation to go the extra mile to meet the EU on the issue.