Prime Minister Malcolm Turnbull and Treasurer Scott Morrison. Credit:Andrew Meares In short order, the Coalition struck a deal with Labor to pass most, but not all, of the so-called omnibus savings measures through the Parliament. Soon after that, cabinet has bent over backwards, twice, to do deals with its own restive backbench on policy. The first was the controversial superannuation changes that Mr Turnbull described during the campaign as "ironclad" – and for which the government arguably had the same "mandate" to deliver from voters. The second, on Tuesday, was a backdown on the so-called backpacker tax. In both cases, Treasurer Scott Morrison compromised.

Liberal MP Warren Entsch with Greens senator Sarah Hanson-Young and independent MP Cathy McGowan after he introduced a private member's bill for marriage equality to Parliament House in August 2015. Credit:Andrew Meares Importantly for him, the budget has been left no worse off, and as the Treasurer argued "we are a government that solve practical problems, and gets on with the job". So why, Labor asks, is the government prepared to back down on changing the super package, and on some of its savings measures, but not the plebiscite? Opposition Leader Bill Shorten and Labor spokeswoman for equality Terri Butler. Credit:Dominic Lorrimer It's a fair question, and one not only being asked by the opposition.

In part, the answer is this: the Turnbull government is keenly aware of its one seat majority in the lower house. The precipitous slump in support for the plebiscite effectively denies the government one of the arguments it has relied on to make the case for the national opinion poll. If it were to back down on the plebiscite plan all hell would break loose in the Coalition party room. Labor knows this and, politically, it suits the opposition to give no quarter on the plebiscite. In that context, Tuesday's Newspoll was a gift for the ALP.

The poll punctured the second strand of the government's pro-plebiscite argument – that it is popular with voters, who want to decide the issue themselves. On July 1, the eve of the election, a Fairfax-Ipsos poll showed fully 69 per cent of voters supported a plebiscite, rather than a politician's vote, to decide the issue. That support has now crashed to just 39 per cent, according to Newspoll, while 48 per cent now favour MPs voting on the issue in Parliament. It could not have come at a worse time for the Coalition, which is doing its best to take the fight to Labor but facing strong headwinds as it attempts to win the public debate over the plebiscite. Make no mistake, the stand-off over how to resolve the same-sex marriage question is a failure of both sides of politics.

But the precipitous slump in support for the plebiscite effectively denies the government one of the arguments it has relied on to make the case for the national opinion poll. Its willingness to compromise on other policy questions leaves it exposed. Mr Morrison was ready to pivot on Wednesday, when asked about the plebiscite's dwindling support. "Do you accept that public support for the plebiscite is dwindling and that the people are not listening to the Turnbull government on the way forward on same sex marriage?" "I accept that the government put to the Australian people the proposal for a plebiscite that was endorsed at the general election and I back the mandate of a general election," Mr Morrison fired back.

But Bill Shorten's riposte was blunt, and on point: "...wake up Malcolm Turnbull, listen to the Australian people, stop listening to the far right of your party, do not waste $200 million on a marriage equality opinion poll which you can't even make your backbenchers agree to vote for once people have to vote in the plebiscite." The government is, strictly speaking, correct to argue it has a mandate for a plebiscite as it was returned, albeit with the slimmest of majorities. But Labor and the crossbench can equally argue they have support from the cohort of people who voted for them for their stance. In the Senate, where the government holds just 30 of the 76 seats, it is a powerful counter-argument. As the government continues to compromise on other policies to get things done, its refusal to move on the plebiscite will be harder to justify. And as public support for the national poll falls, the plebiscite increasingly looks like an expensive albatross around the neck of Turnbull and co.