We don’t like the carbon tax any more since legislation passed the House of Representatives. But we don’t like it any less after the perceived unseemliness of the triumphalism that followed its passage.

That’s the message in new polling from Essential Research, which shows little change in the level of support for Labor’s landmark legislative achievement.

Conducted between Wednesday and Sunday, the online survey of 1047 respondents shows 39% supporting the carbon tax against 53% opposed. This is slightly better for the government than the Galaxy poll in today’s News Limited tabloids (34% support and 57% oppose), but effectively unchanged on Essential’s survey of September 19. And it continues a pattern where Essential Research’s online panel methodology has consistently produced less unfavourable results on this issue than phone polls.

Essential also gave respondents three options for what should happen to the tax if Labor is defeated at the next election, in contrast to Galaxy’s approach of asking whether a victorious Tony Abbott would have a mandate for its repeal (to which 60% said yes).

Thirty-four per cent favoured a double dissolution to secure the repeal of the tax, with 33% prepared to allow that the tax should remain “if it proves to be effective in reducing carbon pollution”. More than 20% felt it should remain in any case “to provide certainty for individuals and business”. As always with questions related to the carbon tax, a strong polarity was recorded between Coalition and Labor/Greens voters.

Respondents were also asked to take their pick from 12 options to describe the positions taken by the leaders on asylum seekers, and the results provide consistently unflattering reading for Julia Gillard. The bitterest pill would be that she outscored Abbott on both “too soft” (21% to 7%) and “too hard” (10% to 6%).

Abbott even managed to record an effectively equal score to Gillard on his traditional negative of “just playing politics” (47% to Gillard’s 46%).

There is some relatively good news for the prime minister on the monthly measure of leaders’ personal ratings, in the shape of an 11-point improvement in her net approval rating after a disastrous showing in the September 12 poll. Gillard’s approval is up six points to 34% and her disapproval down five to 59%, and her deficit on better prime minister is down from four points (40% to 36%) to one (39% to 38%).

Abbott’s ratings have recorded no significant change: his approval and disapproval are both up one, to 40% and 51% respectively.

On voting intention, the major parties have recorded no change on last week’s result. The Coalition continues to lead 48% to 33% on the primary vote and 55% to 45% on two-party preferred, with the Greens up a point to 11%.