There is strong support for several of Labor’s major policies, despite its parlous polling situation, new polling finds.

More than half (53%) of voters back the government’s means test for the private health insurance rebate, according to Essential Research’s weekly online poll of 1000-plus voters, with a third (33%) of responders opposing it.

Support is strongest among Labor voters at 76%, while 51% of Liberal voters oppose the means test. Support is also strong among lower income groups: people earning $31,200 to $51,999 annually run at 63-23%, while the key beneficiaries of an unmeans-tested handout, those on incomes over $83,200, split almost equally at 45-46%.

Support for the National Broadband Network has also strengthened a little, with 56% of voters in favour and 25% opposed — a small shift since April last year and the highest level of support since immediately after the 2010 election. Labor and Greens voters are both strongly in favour of the project, while Liberal voters are nearly evenly split.

Support for the mining tax has also increased, up four points since November to 55%, while opposition has fallen five points to 28%. It appears the passage of the tax through the House of Representatives late last year has crystallised support; as late as September the tax only had 46-34% support.

But that’s where the good news ends for Labor: it has lost a point on its primary vote, falling to 33%, while the Coalition and the Greens have both picked one up to move to 48% and 11% respectively. While the changes are within the margin of error, the two-party preferred outcome shifts to 55-45%.

It appears that, whatever is wrong with Labor, it’s nothing to do with its policies: apart from the carbon pricing package, its key policies all garner strong support.