This poll is another shocking result for Gillard. Her personal authority continues to erode. People have not got over her knifing of Kevin Rudd: this is indicated by the former PM's huge lead in a head-to-head contest. (Indeed the poll suggests that, regardless of the parties' views, the public would like the Rudd-Turnbull contest they were denied last time.)

Equally alarming for Labor, putting a price on carbon - the issue currently of most importance to the government - continues to get more unpopular.

While it is true governments easily lose support when they get into difficult arguments, Gillard has no electoral margin to cushion her. Although the carbon tax should be well in place when she faces voters, a debilitating fight could have taken an irreversible toll. Pulling up a 31 per cent ALP primary vote (its lowest since 1996) is a massive challenge.

The increasing public opposition to the carbon price (44 per cent in February; 59 per cent now) comes as the union movement is starting to panic and business is hyping up its compensation demands. The poll will strengthen the carbon tax's opponents and those agitating for the best deal for themselves.

For Labor, the worst is that it is boxed in. It can't dump a second PM. It can't retreat on a carbon price for a second time; it can only arbitrate as best it can between the competing claims and make its case to the public as effectively as possible.

The bad poll puts extra weight on the May 10 budget. Gillard has set a high bar for herself, talking up her reform package to get people from welfare to work.

If this disappoints by being a damp squib or too harsh, she'll either be condemned for not delivering or have a fresh row on her hands.

It's clear the government's onslaught on Abbott's negativity isn't working. Indeed, Labor might do better to obsess a little less over the opposition at this point in the political cycle - it may just underline Labor's insecurity.