Eighteen months ago, an American named Gus Speth, described by Time as the "ultimate insider" for his string of public and academic appointments, was arrested in Washington DC at a protest against the Keystone XL pipeline, which will carry Canadian crude oil to America's oil refineries. From jail he said: "I've held numerous positions and public office in Washington, but my current position feels like one of the most important."

A year later, delegates at the Republican party convention roared with laughter as Mitt Romney suggested that while he would help voters and their families, Obama was merely promising to try to lower sea levels and heal the planet. It seemed like Professor Speth and the climate expert James Hansen, arrested with him, were ridiculously out of touch with what the vast number of Americans believed and it would take a generation or more to persuade the country that "the world is firmly on the path to a ruined planet in the lives of today's children", as Speth has written.

But things seem to be changing rapidly in the US and that may just help create the circumstances for a new carbon tax, which is aimed at controlling the rise in global temperatures and which, astonishingly, might be acceptable to conservatives. The opportunity arises, however, not because conservatives have moved lockstep into Obama's camp, but principally because of America's vast budget deficit and the approaching fiscal cliff.

Even so, attitudes are on the move at a spectacular pace. Two years ago, just 57% of Americans believed climate change was happening. By March this year, the number had risen to 66% and by September to 70%. That survey was taken a month before tropical storm Sandy hit New Jersey and New York, but after a series of heatwaves and wildfires, the Oklahoma dust storm, crop failure and the unprecedented drought, it is clear that the penny has dropped about extreme weather events.

For the first time in this debate in the US, the majority seems convinced that self-interest is best served by belief rather than denial. Not before time. Whatever the deniers and sceptics say, and there are still plenty of them in the US and Britain, the science of climate change is returning some worrying figures, which seem to presage a rise of well over 2% in global temperatures by the end of the century.

The evidence is impressively varied. Sea levels are rising more sharply than predicted by the Intergovernmental Panel on Climate Change, in fact, 60% faster. Polar ice is melting three times faster than in the 1990s, according to research published last week by the US National Snow and Ice Data Centre. High pressure anomalies over Greenland have been affecting the climate of North America and northern Europe since 2007, with many knock-on effects. Last week, it was reported that acidification of the sea, caused by absorption of CO2, is now corroding the shells of tiny marine snails, which are an essential part of the food web. And in North America, the drought, which now threatens next year's crop of winter wheat, shows no sign of ending. This year has recorded a drop of 3% in farmers' incomes and crop insurers have already paid out $6.3bn.

Deniers will find alternative explanations for these events, chiefly that scientists have an incentive to talk up global warming while ignoring the chaotic nature of the Earth's weather systems, where anomaly is the rule. But the evidence is almost incontrovertible, in the words of the former Cambridge economist and now consultant Dr John Llewellyn, who has written about the economic impact of climate change. We should accept that the trend is not good and take the acceleration of the crisis seriously.

As to the new carbon tax and its potential benefits, it is important to say that it is not a done deal. Indeed, its supporters are anxious not to raise the subject too publicly, for fear of provoking an irrational spasm from the right. But a carbon tax could be a way of avoiding a steep rise in income tax and save cuts to Medicare, Medicaid and social security, the prospect that haunts Washington as the 2 January deadline for a budget deal looms. It is estimated that a tax of $20 per ton of carbon emitted from 2013, with an increase of 4% per annum, will raise $1.25tn in the next decade and reduce emissions by 14% below 2006 levels.

Another tax may not seem a great idea, but this has the virtue of simplicity, unlike the various tax and emission capping schemes in Europe, where, incidentally, there is a reversion to the worst pollutant – coal – even though the continent signed up to the Kyoto agreement. The carbon tax would introduce choice and the wisdom of the marketplace, very much along the lines advocated by the Oxford economist Dieter Helm in his book The Carbon Crunch. Its advantages are that it will have an impact on heavily polluting manufacturers outside America, as well as within the US, reduce excessive trade and return jobs to the US. Nature magazine estimates that the money going to clean energy research could rise 10 times, to $30bn annually.

The most surprising fact in this hushed debate is that the ultra-conservative American Enterprise Institute is prepared to contemplate the idea and Grover Norquist, president of Americans for Tax Reform, has murmured that a carbon tax would not violate his principles. Republicans might be persuadable, even though the oil and coal industries will oppose the idea vigorously. But the lobbyists don't have much time, if this is to be part of the budget deal, and it is now well understood that $500bn in budget cuts represents about a million American jobs. With the change in American public attitudes to global warming, the rapid transition to cheap and less polluting shale gas, the pressure on budget and jobs, this just could be the perfect moment for something approaching meaningful action.

The vital point is that a price on carbon in the US will have a dramatic geopolitical impact, as Dieter Helm and John Llewellyn independently point out. Europe is in a muddle of cap and trading, with each country doing its own thing, but it is at least actively trying to reduce emissions. With a settled carbon price in the US, countries with half the world's GDP will be working in a more or less consistent direction. America will look amazingly good compared to the shambolic arrangements in Europe and downright saintly compared to China.

Yet we have to understand that none of this may be enough and that our attitudes to energy saving, social equity, personal consumption and endless growth may have to change to prevent global temperatures rising by that supremely destructive 4C.