Labor has strengthened its primary vote at the expense of the Coalition and edged ahead on the 2PP vote for the first time since the last weeks of the election campaign. For weeks the Essential Report poll has had the major parties locked together on 2PP, but this week Labor has moved to a 51-49 lead (based on a two-week rolling sample) on the back of a small lift in its primary vote to 42% and a fall for the Coalition to 43%. The Greens remain unchanged on their (comparatively low) 9%.

Essential asked voters’ views on the National Broadband Network and found very strong support for it, with 56% of voters backing it, including more than a quarter “strongly in favour” and only 18% opposed. Liberal voters were notably cooler on the NBN, with 38% opposing, but 31% of Liberal voters also back it. “Don’t knows” were noticeable higher among Liberal voters, with 30% declining to offer an opinion, suggesting the Government could shift a substantial bloc of support for the project if it can figure out how to sell the benefits of the NBN, or for that matter any of its policies.

Julia Gillard’s decision to abandon her “no carbon tax” stance as a consequence of minority government doesn’t appear to have hurt her: despite the Coalition saying Gillard has broken a clear promise, 63% of voters rated it as important that the Government move “quickly” on an ETS or carbon tax, including 37% who rated it as a top priority or very important.

And here the partisan divide was less clear, because while support for quick action is very strong amongst Greens (40% of whom say it’s a top priority) and Labor, 42% of Liberal voters thought quick action on a carbon price was important, including 20% who thought it was a top priority or very important.

There’s also very strong support — 69% — for laws to be changed to allow euthanasia at the request of patients with incurable disease and severe pain.

There’s better news for Tony Abbott on comparative leadership: he leads Malcolm Turnbull by 26-20% on the question of who would make the best leader of the Liberal Party, with Joe Hockey third on 15%. However, Abbott has a huge lead, nearly 40 points, over Turnbull among Liberal voters, and in fact they prefer Hockey over Turnbull anyway, 17-15%.