Locals call this city "carbon central". But in the polarised Australian climate change debate, this mining hub is not central at all, but firmly positioned at one extreme.

Wollongong, 50 miles south of Sydney in New South Wales, is home to 300,000 people and millions of tonnes of coal.

The steep hills around Wollongong afford views of endless queues of ships on the watery horizon, waiting for their cargo of black gold. Coal has been the lifeblood of the city for 150 years and the backbone of its steel industry.

Regardless of the climate extremes, the droughts, wildfires, cyclones and floods that are ravaging Australia, locals do not want to give it up.

"It's all right for greenies to say this carbon tax has to happen, but we can't all hug trees for a living," said Brett Withers, who has worked as an industrial cleaning contractor in the steelworks for 20 years. "It might just be the straw that breaks the camel's back. If the tax comes in, this area will be devastated. It's not just the steel industry - it's the butcher, the hairdresser and the baker. Everyone will suffer."

Withers' remarks illustrate a furious backlash against imminent government plans to introduce a carbon tax. Labor prime minister Julia Gillard plans to announce the level of tax to be levied on pollution on Sunday 10 July.

The levy was proposed by Gillard, who needed support from Greens in a hung parliament. But the plan has divided Australia like no other issue of recent years.

An opinion poll on Tuesday 28 June showed Gillard's disapproval rating at 62%. Another poll suggested barely one in four Australians would vote for her, making her government the most unpopular in 40 years.

Cities such as Wollongong have led the assault, as blue collar voters - who have done well on the back of the mining boom - desert the prime minister in droves.

Australia is the world's largest exporter of iron ore and coal, much of it bound for China and Japan. As commodity prices have skyrocketed, so have profits.

Australia's commodity export earnings are expected to rise 18% to a record $270bn (£180bn) in the next year. It is an industry that sustains a lot of livelihoods, and a lot of voters.

"If the polls as they stand now persist, then Labor will suffer a landslide thrashing in two years' time," said Nick Economou, senior lecturer in politics at Melbourne's Monash University. "They're in terrible, terrible trouble."

Gillard is not the first Australian leader to be unsettled by the climate and carbon debate. Her predecessor, Kevin Rudd, dropped his planned emissions trading scheme after failing to get it through parliament. It was the beginning of the end of his tenure.

In last year's election campaign, Gillard promised there would be no carbon tax if she was elected. But then came the hung parliament, with a majority of just one. With her political survival suddenly based on support from the Greens, she quickly changed her mind.

"You're really going to test the credulity of the electorate if you say one thing on a carbon tax and then do another," said Economou.

Post-election, Gillard set up a multi-party committee to hammer out details of the carbon tax. The scheme will start with a government-fixed price on carbon, moving to a market-set price after three years. The committee is expected to finalise the details of the tax within days but negotiations have dragged on for months, further damaging the government's credibility.

Over the weekend, Gillard announced that petrol would not be included in the tax but there is still no certainty on what the price of carbon will be under the scheme, which industries will be in or out and, crucially, what the compensation to households will be.

Gillard's standing has taken a battering and many voters have stopped listening to her.

The conservative opposition - led by climate sceptic, Tony Abbott, who once described human-induced climate change as "crap" - has capitalised on the uncertainty and on Gillard's flip-flop.

His slogan about a "great big new tax on everything" has been drilled home, along with the message that a carbon tax will hurt ordinary Australians.

His party has proposed "direct action" to meet the bipartisan agreed target of reducing CO² emissions by 5% by 2020 (based on 1990 levels). Abbott's voluntary scheme includes, among other things, planting 20m trees.

Rightwing shock jocks have also rammed home the anti-tax message, arguing that whatever Australia does will make little difference to the world's climate.

They have called Gillard "Ju-liar" and launched scathing personal attacks on senior government advisers on climate change as well as scientists. Some have even been subjected to death threats.

The growing number of climate change deniers put recent events like this year's devastating floods in Queensland and the most powerful cyclone in Australia's history (cyclone Yasi in February 2011 was as powerful as hurricane Katrina) down to freaks of nature rather than climate change.

From his inner city veggie patch stocked with lettuce, beetroot and cabbage, Sydney resident Greg Bearup despairs at the government's handling of the carbon tax debate. "I just can't see how we went from 60-70% support for action on climate change to a position where Gillard looks like she could lose her job over it," he said. "It's unbelievable it could have been handled so badly."

Bearup's street is just 15 minutes from the centre of the city, but a world away from the glistening blue of the harbour. The area has been gentrified but remains a concrete jungle with first world war era houses.

Two years ago Bearup and his neighbours dug up the concrete in front of their homes and planted gardens. He says the concrete was acting as a heat bank. Removing it has lowered the temperature in the summer, reducing the need for air conditioning.

He said a carbon tax will make sure heavy polluting industries like mining pay their fair share for the damage they are causing to the environment. "Everyone should be making an individual contribution to tackling climate change," he said.

• This article was amended on 5 July 2011. The original said that Australia is the world's largest producer of iron ore and coal, much of it bound for China's hungry construction industry. This has been corrected.