A RARE moment of triumph settled on Julia Gillard, Australia's prime minister, on July 10th when she unveiled a plan for a carbon tax to fight climate change. Few issues have divided Australians more bitterly. Earlier plans to curb carbon emissions had toppled at least two political leaders, including Kevin Rudd, Ms Gillard's Labor predecessor. She justly boasted that she had knocked down the brick walls others had hit. But then political reality kicked in. An opinion poll two days later (conducted before the carbon plan's details were disclosed) gave the Labor government record low support of 27%. With the next election due in two years, Ms Gillard faces the task of rescuing her government by selling her bold carbon plan to a sceptical public (see chart).

Australians have not always been so cynical on the subject. Four years ago, Mr Rudd's promise to tackle climate change helped him defeat a conservative Liberal-National government. Voters seemed to respond to a central argument: that Australia's credibility as a clean-energy advocate in the Asia-Pacific region would count for little unless it cut its own relatively high carbon emissions first.

Australia emits 1.5% of the world's greenhouse gases primarily because it generates about 80% of its electricity from coal, one of the dirtiest sources of power. It is roughly as polluting as South Korea, Britain and France, which have populations two to three times Australia's 22m people—making Australia the biggest carbon emitter per person of any rich country. And climate change has not been ruled out as a cause of its recent bouts of extreme weather: a ten-year drought, and floods and cyclones early this year. The National Australia Bank, a private bank, says the economy is “still struggling to find traction” since the flood-induced slowdown.

When the Lowy Institute, a think-tank, asked Australians to nominate their country's most important foreign-policy goals in 2007, the year Mr Rudd swept to power, “tackling climate change” topped the list. In the same poll this year, that goal dropped to tenth place; first now was “protecting the jobs of Australian workers”. For a country with an envious unemployment rate of 4.9%, it seemed an odd change in priorities. But it reflected, perhaps, the shifting dynamics of climate politics.

Mr Rudd came within a whisker of snaring bipartisan support for a market-based scheme to cut carbon pollution. But he failed after the Liberal-National opposition and the Australian Greens formed an unholy alliance to reject it in parliament. After Ms Gillard deposed Mr Rudd as leader, she promised not to introduce a carbon tax. But last August an election left her leading a minority government and relying on independents and Greens for survival. One price the Greens demanded was a multiparty parliamentary committee to devise a fresh climate plan (the opposition coalition boycotted the committee). The plan Ms Gillard has announced largely reflects that committee's consensus.

From next July 500 of Australia's biggest polluters will have to pay a tax of A$23 ($25) a tonne on their own carbon emissions. Three years later, a market-based emissions-trading scheme will replace a fixed tax. The government will spend half the tax's revenue compensating households for higher electricity and other living costs that polluters pass on. Another 40% of revenue will help industries to lower their costs by switching to cleaner forms of energy, if they face competition from untaxed foreign competitors. About A$10 billion will be invested over five years in wind, solar and other renewable sources. And Australia now aims to cut its emissions by 80% of their 2000 levels by 2050 instead of 60%, Labor's previous figure.

The Greens and three independents have pledged Ms Gillard the votes to get the plan through parliament later this year. Winning back public trust on climate action is her bigger worry. A raucous chorus of radio “shock jocks” and tabloid journalists has accused Ms Gillard over her broken promise and echoed a campaign by Tony Abbott, the opposition leader, who is warning about the tax's possible impact on jobs and the cost of living.

Yet the political currents are capricious. Mr Abbott kicked off his attack in the Hunter Valley, a coal-mining region of New South Wales, where he branded the tax a threat to coal's future. The claim deflated within a day when Peabody Energy, an American coal company, and Arcelor Mittal, a steelmaker, launched an A$4.7 billion takeover bid for Macarthur Coal, a big Australian miner that sells coal to steel mills in Asia, Europe and Brazil. Greg Combet, the minister for climate change, says 19 new coal mines are due to open in Australia; the tax could encourage them to capture methane, a carbon gas emitted in coal-mining.

Business reaction has been mixed. Some big resource companies and banks, which stand to do well from new markets in emissions permits and renewable energy, have supported the plan. New Zealand, which has introduced its own carbon price, has welcomed the prospect of a trans-Tasman carbon market.

Christine Milne, a Greens parliamentarian, reckons Australia's plan will boost incentives for China and South Korea, which are exploring market-based anti-carbon mechanisms themselves. Ross Garnaut, an economist who advised the government, says the sceptics' line that Australia has no influence on what others do is “a path into quicksand”. But suburban and rural Australia is where the political battle will be won or lost. That is where Ms Gillard's negotiating skills now face their biggest test.