There is growing opposition to the carbon tax after the House of Representatives passed bills for the scheme, a Newspoll has found.
Opposition to the tax has jumped six percentage points to 59 per cent, the poll commissioned by The Australian has found.
Support for the tax has fallen four points to 32 per cent.
But it's not all bad news for Labor, with the poll showing there was a four-point drop in the Coalition's primary vote to 45 per cent, the lowest since May this year.
The Greens climbed back to a record 15 per cent primary vote support, rising three points.
Prime Minister Julia Gillard's personal satisfaction with voters rose three percentage points to 31 per cent.
Opposition Leader Tony Abbott's rating was down from 36 per cent to 34 per cent.
However, Mr Abbott still maintained the lead as preferred prime minister at 39 per cent compared with Ms Gillard's 36 per cent.
Newspoll chief Martin O'Shannessy said Labor's primary vote was stuck on 29 per cent, unchanged from two weeks ago while the Coalition's loss of support had mostly gone to the Greens.
Ms Gillard might take heart from the improvement in her approval rating, he said.
But continuing opposition to the carbon tax made it hard to accept the government's view that the passage of its legislation through Parliament would improve Labor's position.
"We have been tracking this now for a while. Back in April-May it was 60, in July 59," Mr O'Shannessy told ABC Radio.
The latest Newspoll has opposition to the carbon tax still at 59 per cent.
Parliamentary secretary Kate Lundy believes commonsense will prevail on the carbon tax.
"This policy is embedded in good science," she told Sky News.
"I think the opposition is starting to be exposed in the lack of sincerity in their fear campaign."
People were starting to question the opposition's motivation, knowing it was about "dirty politics" not policy.
Opposition frontbencher George Brandis said the Coalition was "very, very happy" about the latest Newspoll.
"For the Labor Party to find comfort from the fact they're only 16 [percentage points] behind the Coalition on the primary vote ... just goes to show how desperate the Labor Party's situation has become," he said.
Senator Brandis rejected any suggestion the Coalition was playing politics over the carbon tax.
"We simply think it is a stupid idea and, by a majority to two to one, so do the Australian people."
