A new opinion poll underscores the substantial political difficulties associated with some of the more ambitious reform proposals that could emerge from the Abbott government’s new commission of audit process.

An Essential poll published on Tuesday shows public disquiet with a number of the potential directions floated in the lead-up to the creation of the new commission of audit – the first inquiry of its type at the federal level since 1996.

The Coalition has allowed the commission, chaired by business chief Tony Shepherd, to embark on its work with very broad-ranging terms of reference.

The government has been careful not to pre-emptively rule options out in advance – although during the election campaign, the then shadow communications spokesman Malcolm Turnbull told the communications union the Coalition had no plans to sell off the postal service.

Treasurer Joe Hockey has made it plain the commission needs a broad canvas on which to work. The context for setting up the inquiry was the Coalition’s oft repeated declarations of a “budget emergency” – which created a requirement to find substantial efficiencies to bring the federal budget back to a sustainable footing.

The prime minister has said the commission is very unlikely to propose tax increases, setting up the proposition that the budget sustainability sought by the new government will be driven by reducing the size of government, eliminating duplication and cutting expenditure.

The new Essential poll shows 63% of the sample would oppose the sell-off of Australia Post; 59% would oppose the privatisation of the Hecs debt (an option left open by the education minister, Christopher Pyne); 60% would oppose cutting welfare benefits; and 59% would oppose handing control of DisabilityCare to a privatised Medibank Private.

The poll also suggests mixed public views about the Abbott government’s plans to privatise Medibank Private. Of those questioned, 43% opposed the privatisation, 22% supported it, and 35% didn’t have a view.

There was, however, strong public support for potential recommendations reducing duplication between the states in areas like education and health (73% were in favour); and the means testing of all welfare benefits (63% support).

How the Abbott government responds to suggestions flowing from its commission audit will be a significant test of its early political resolve. The prime minister used a recent radio interview to begin laying the groundwork for what might emerge when the commission hands down its findings in 2014.

“If we are going to get debt under control, if we are going to get the budget under control – back into the black – yes, inevitably, things will have to change,” Abbott said last month.

“There will be some things the public don't like but I think the public understands the government has been living beyond its means. We can't continue. And that’s why, amongst other things, we are having this commission of audit.”