Liberal voters prefer Tony Abbott, but everyone else would prefer that Malcolm Turnbull resume the leadership of the Liberal Party, today's Essential Report shows.

As the spat between Communications Minister Malcolm Turnbull and reactionary blogger Andrew Bolt threatens to set Liberal leadership hares running, Turnbull enjoys a big advantage over Prime Minister Tony Abbott among voters, this week’s Essential Report shows.

Turnbull is considered “best leader of the Liberal Party” by 31% of voters, compared to 18% of voters who prefer Abbott. The other popular figure is “someone else”, who actually beats Abbott, on 19%.

However, Turnbull’s strong performance is a big come down from 10 months ago: at the end of July 2013, 37% of voters preferred him, compared to 17% who preferred Abbott.

Liberal voters strongly prefer Abbott, by 43% to 27%, while Labor and Greens voters prefer Turnbull by around 36% to 3%; “other” voters rate Turnbull ahead of Abbott 28% to 13%. Women are unenthused by both: 15% of female voters prefer Abbott and 28% prefer Turnbull, compared to 21% and 33% for men.

Treasurer Joe Hockey is preferred by just 6%, a far cry from 2011, when Hockey rivaled Turnbull in popularity as an alternative leader, and down from 10% last year. Julie Bishop is on 4%; Christopher Pyne, Andrew Robb and Scott Morrison are all on 1% or less. “Someone else” is the big improver, having managed only 12% last year.

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The poll also shows the Labor continuing to recover in the esteem of voters in relation to policy issues. Voters trust the Coalition to manage the economy 41%-28%, but that 13-point gap between the parties is down from 19 points in February; Labor has significantly increased its lead as the party trusted to ensure the quality of the health system, from 2 points to 13 points; it widened its lead on education from 7 to 15 points and lifted its lead as the party trusted to protect Australian jobs and local industries from 2 points to 12 points. It has also cut the Coalition’s lead on several issues: the Coalition now leads on “political leadership” by 6 points, down from 13 points; on interest rates the Coalition lead has fallen from 17 points to 12 points; on “ensuring a fair taxation system” the Coalition’s 6 point lead is now just 1. Only on asylum seekers, national security and population growth has the Coalition maintained its lead.

Voters are divided, however, on whether Labor should block the budget with the aim of forcing an election: 47% support that, compared to 40% who do not, but that reflects a strong partisan split among voters. Forty-eight per cent of voters believe the budget cuts spending by too much; 11% believe it didn’t go too far, and 21% believe it cut spending the right amount. That is a noticeable change from the week after the budget, when 41% thought the budget went too far and 26% thought it was just right, suggesting the government had gone backwards in the one area where it had been successful in its budget sales message, convincing voters of the need for tough fiscal measures.

But 63% of voters want Labor to block deregulation of higher education fees; 61% want the Medicare co-payment blocked; 62% want the pension rise to 70 blocked, 57% want the cut in funding to universities cut. But 47% of people want Labor to support the six month waiting period for Newstart recipients, compared to 41% who want it blocked; 64% want the requirement for graduates to repay HELP loans sooner supported; 65% want Labor to back the foreign aid cut and 73% want to deficit levy passed.

On voting intention, Labor now leads the Coalition on primary vote for the first time since May 2010: Labor remains on 39%, but the Coalition has slipped two points to 38%; the Greens have gained a point to move to 10%; the Palmer United Party has gained one to move to 6%. The extends Labor’s two-party preferred lead to 53-47.