Australian Prime Minister Julia Gillard faces popular rebellion on key economic policies that could prompt their reversal if Labor loses power in the next election.
This includes the carbon tax due to begin on July 1 and its later evolution to an emissions trading scheme, and increasing foreign investment in mining and agricultural land, especially from China.
The latest annual Lowy Institute poll also shows Australians place little faith in the Government's economic management, believing instead the minerals boom saved the nation from recession.
The poll's findings on climate change policies present the most urgent issue for Gillard.
The Opposition has maintained an unrelenting attack on the carbon tax - warning of soaring increases in business and household costs - and has promised to repeal it if they defeat Labor.
Gillard has struggled with the policy since she backflipped on earlier campaign promises and announced its introduction after the formation of her minority Government in 2010.
The Lowy poll said that Australians were softening their views on measures to fight global warming, with support for urgent and strong policies falling from two-thirds to 36 per cent in the past six years.
The strongest support, of 45 per cent, now lies with an "intermediate" approach that acknowledges the need to address climate change, but through gradual, low-cost options.
The poll said 63 per cent of Australians opposed a fixed carbon price leading to an ETS, with more than half believing it would cost jobs, and 38 per cent saying it was not necessary to act before other countries.
One-third opposed the move because it did not go far enough and lacked measures strict enough to substantially reduce emissions.
Opinion is fairly evenly divided on the Opposition's promise to repeal the legislation - but the 38 per cent who support its removal cross all states, age groups, income levels and both genders, with significant support from Greens voters.
Nor has the Government sold its economic credentials to voters.
The poll said 70 per cent said Australia managed to avoid falling into recession because of demand for resources from countries such as China, rather than astute Government management.
But more than half believe the Government is allowing too much Chinese investment.
It said the two greatest reservations were fears for the future control of crucial mining and agricultural assets. The poll said 81 per cent of Australians opposed the sale of farmland to foreigners.
But most support Labor's controversial new short-term migration agreements allowing miners to import skilled workers to fill gaps in the local workforce.
The poll said 62 per cent favoured admitting extra workers when "there are shortages of workers in Australia and companies in Australia cannot find enough skilled workers".