Labor’s primary vote under Prime Minister Kevin Rudd appears to have stabilised just short of 40%, leaving the Coalition with a narrow but election-winning lead, today’s Essential Report reveals.

However, Rudd has dramatically reversed the slide in Labor’s reputation across a range of key issues.

With speculation an election might be called as soon as this week, Labor’s primary vote remains unchanged on 39%, the Coalition has dropped a point to 45%, and the Greens remain in parlous territory on 7%. The two-party preferred outcome is 51%-49% to the Coalition, a little down on last week’s 52-48 result.

Essential repeated its questions about trust in parties’ handling of issues, asked just before Julia Gillard was removed as prime minister. Labor has improved three points on economic management (it trails the Coalition by 15 points), significantly increased its lead on education (from 1 to 9 points), moved to a small lead on health (from -5 to 1), picked up significantly on industrial relations (3 to 11), improved on Australian jobs and protection (-7 to -1), addressed the leadership issue (-19 to -7) and slashed the Coalition’s lead on asylum seekers from 22 points to 11 points.

Voters also support Rudd’s decision to move earlier to an emissions trading scheme, 45% to 29%, with both Liberal and Labor voters endorsing the shift and only Greens voters opposed.

The results suggest Opposition Leader Tony Abbott and the Coalition would narrowly win an election despite Rudd dramatically revising voters’ perceptions of the ALP. The judgement call for the Labor brains trust will be whether this is as good as it will get for them and they should go to an election now, or whether Rudd can wear down Abbott and gets Labor’s primary vote over 40%, at which it would be in a strong position to pull off a remarkable victory.

Voters were also asked about support for a referendum to recognise Aboriginal and Torres Strait Islanders and outlaw racial discrimination in the constitution. Some 62% of voters supported it, and 16% were opposed; 23% didn’t know. Greens voters were most likely to support it (80%); 56% of Liberal voters supported it, 21% opposed it.