From her own mouth she is condemned

"There will be no carbon tax under the government I lead" declared Julia Gillard shortly before the last federal election, that saw Labor cling to office after cobbling together an unlikely alliance with a Green, a former Green and two rural independents.

Like Kevin Rudd's 2007 commitment to being an "economic conservative", this declaration was aimed at reassuring the voters and heading off a scare campaign by the Coalition. And like Rudd's pledge, Gillard's promise has turned out to be quite untrue.

I'm sure Tony Abbott can hardly believe his luck. As well as being able to call the Prime Minister a liar, he can also run the "great big new tax on everything" line which frightened Rudd and resulted in the government ditching its Emissions Trading Scheme before the 2010 election.

As question time last week showed, Abbott, a former pugilist, is going to be an even more ferocious Opposition Leader than usual, continually looking to knock the government out by throwing vicious uppercuts and big overhand rights.

The stakes could not be higher for Gillard as the real question is whether her leadership can survive. Since Labor disposed of Kevin Rudd's Prime Ministership last year it is certain that if the tax is confirmed as a serious electoral liability, Gillard's leadership will be similarly terminated as part of a radical about-face for the government.

The newspoll figures just released confirm that Labor is in trouble as a result of the carbon price plan, with most voters opposed and Labor's scores in the primary vote and two party-preferred slipping badly. There is little doubt that winning over the public's acceptance will be an uphill struggle.

Some have compared Gillard's carbon tax to the GST, but the Howard Government gave the people the chance to vote on its GST proposal at the 1998 election. The better comparison is with Workchoices, as pointed out by Peter van Onselen. But even with Workchoices, the Coalition at least did not specifically promise not to bring it in. The circumstances in which Gillard has introduced her carbon tax no doubt aggravate the anger and betrayal felt by some voters.

It is probable that Gillard's decision to introduce a carbon tax reflects the desire within the ALP to increase its primary vote, which has hovered to low levels for over a year. But the Greens are determined to take the credit for the carbon tax, with Christine Milne claiming that it would not have occurred but for the Greens.

It would therefore appear that Gillard's move has only helped the Greens, with supporters of a carbon tax only more likely to continue voting for the minority party because of its success in achieving a price on carbon.

Meanwhile, the details of the scheme are yet to be worked out, and the Prime Minister must be hoping that enough people study the details once they are released, so that they understand how they will be affected and are no longer so angry or afraid. But the softer the scheme is, the less likely the Greens are to support it, and there's no way the tax can be passed without the support of the Greens. In that event, Labor will look like having stuffed up again, by announcing something without being able to implement it. And voters with long memories will remember the broken promise, resulting in Gillard's esteem within the electorate continuing to be eroded.

Gillard's about-face on the carbon tax reflects the differences between the ALP's main supporters: the suburban working and middle classes on the one hand and the inner-city progressives on the other. It was the former that Gillard was pitching to before the election, with her carbon promise, her supposed opposition to gay marriage and support for border security. Post-election and governing with the support of the Greens, Gillard has now committed herself to a carbon tax and was willing to accommodate the Green's aim to allow the territories to legalise gay marriage and euthanasia in a dramatic shift to the left.

Late last year, Michael Costa argued that Gillard's cosying-up to the Greens and the left agenda was a mistake. In typically blunt terms, Costa wrote that: