Last week’s parliamentary ambush may have caught the Turnbull government by surprise, but it seems that most voters saw mischief coming a long way off.

While Labor was winning the first floor vote from the opposition benches in more than 50 years, Essential was polling the public on their expectations for the longevity of the current Coalition.

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The results show that just one third of voters, and only 50% of Coalition supporters expect the government to run full term.

Put in context, that’s fewer people than expected Julia Gillard’s government to go full term, even when she was in the middle of the three-way cage fight with Tony Abbott and Kevin Rudd.

What’s more, the public does not expect the time that Turnbull does have in power to be a great experience either.

Even off the low base of the disastrous Abbott government, just 18% of voters – and only a third of Coalition voters – expect this government to achieve more than its predecessor.

With a bare majority, the obvious reference point for the Turnbull government is that of the Gillard government, an administration that could never quite shake the perceptions that it was illegitimate.

Despite a strong legislative agenda and the support of the crossbenchers, Labor always seemed to be governing on a hair’s breadth; relying on a disowned member and a compromised Speaker to maintain control of the House.

But as the perception of weakness grew, and the internal leaks shaped the public narrative of a government on the ropes, something interesting began to happen.

People began to lose faith, not just in the government, not just in politics, but in public institutions in general. Trust in institutions is a regular index Essential runs – you can see the full trend data here.

We re-ran the Trust Index this week and found the numbers are trending down again, as it did when the Gillard-Abbott death fight was at its height.

As it was in 2012, it isn’t just faith in government that is falling, everyone from the high court to the Reserve Bank to business groups are experiencing a decline in their reputation.

While you could argue that religious organisations and trade unions have been victims of their own (royal) commission, the overall trend-line shows people are losing faith with everything.

This pessimistic attitude is dangerous for incumbents; a lack of faith in institutions affects every issue a government must deal with because these are the institutions that must implement the response.

This lack of faith in public institutions worked against everything the Gillard government attempted: the carbon tax, mining tax, education reforms, even the NDIS were all part of a bigger and more positive vision of government.

While the Gillard agenda needed an optimistic faith in public solutions, Abbott could skilfully knock away at the entire agenda in three word grabs, secure he was fighting against a loveless project.

If anything, the Turnbull government’s challenges are even greater than Gillard’s.

While her government was paralysed by venal personality politics, on most issues of substance there was consensus on Labor’s broad philosophy: climate action (ish), more funds for education, a redistributive orientation.

Labor’s minority government was workable because of this consensus, even as Rudd undermined and Abbott exploited the divisions, the Labor, Green and independents that kept it in power, saw the world in a common frame.

The leader changed (and changed again) but the fundamental agenda remained the same.

Turnbull’s internal divisions are more substantial. While a resentful Abbott is relishing Turnbull’s discomfort, his desire for revenge is not driving the agenda.

Rather, Turnbull is sitting on an ideological fault-line between the conservatives and the small ‘l’ liberals.

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His conservative base is pushing for a softening to racial discrimination laws, blocking any meaningful action on climate change and continuing their quest to frustrate marriage equality.

Turnbull’s inability to resolve these issues internally leaves little positive about his agenda but a blind faith in trickle down economics and trade liberalisation.

Indeed, all that unites this Coalition is the signature union-bashing of the restoration of the ABCC, tighter controls on union governance and the ham-fisted opportunism of the CFA bill.

As the government wades into battle on these pieces of legislation, it can’t explain how it will deal with the issues that are actually driving the collapse of trust in government: rising levels of inequality, industrial-scale corporate tax evasion and a disconnect with the political project.

When a public loses faith in public institutions, parliamentary tactics are the least of a government’s worries.