The plan, borne of a deeply unpopular Commission of Audit, was designed to help pay for Medicare, which then-health minister Peter Dutton insisted was financially unsustainable.

Voters so detested the idea that two years, a prime minister, Treasurer and Health Minister later, current Minister Sussan Ley still finds herself required to back-pedal from the co-payment and reassure voters the Coalition has learned its lesson, frequently telling reporters the co-payment is "dead, buried and cremated."

Privatising Medicare's payment system was another, less prominent brainchild of the Commission of Audit. After the dust had settled on the dumped co-payment, former health minister Peter Dutton asked his department to put out expressions of interest in a bid to test the market for providers in late 2014. Since then, a number of companies are understood to have been waiting for a contract potentially worth billions of dollars.

Reports this week emerged that the Coalition was preparing to implement the recommendation. Labor, well aware that privatising any part of Medicare carries the whiff of past victories, happily followed it, warning of further health cuts, massive job losses, and risks to patients' data.

While no government policy has actually been announced, Ley was quick to assure voters this was not about privatising all of Medicare. Their plan was aimed at improving Medicare's 30-year-old software system for the digital age.

And the department told Senate estimates it was still in the early stages of deciding how to go about doing this. Department Secretary Martin Bowles said: "We could get to the end of this process and [decide] 'That's a great idea but we can do that (ourselves)."

For a plan that has been discussed internally since late 2014, health bureaucrats appear to be charging ahead at great speed. Consultants are being chosen, and bids for a business case for potential privatisation are due in the next two weeks. And while Bowles insists the full plan will not be finished until 2018, he would not rule out any part of it being accounted for in the upcoming May budget.

Nor would he reveal the kinds of changes they were contemplating, citing commercial reasons, but insisted that any external provider – if it is decided they will need one – will not be decided by the budget.

The longer the government takes to release its plan for Medicare and aged care payments, the more time the Opposition has to warn voters of all the hypothetical dangers it could pose.

Outside of politics, there is little outrage to be found. Lobby groups for the medical profession, health consumers and hospitals all agree that Medicare's payment systems could improve. None inherently oppose the idea of doing this in the private sector, provided that patient data can be protected.

The Grattan Institute's health program director Stephen Duckett says it will depend on what the government wants the private sector to do. Provide payment services currently performed by Medicare offices? Put a chip into Medicare cards so pharmacists can find out what other drugs patients are taking? Or even use analytics to detect fraud and over-payments?

The underlying question of whether completely outsourcing Medicare payments is needed, given that internationally, no other country has done this, also remains to be answered.

Margaret Faux, founder of medical billing firm Synapse, warns there are real concerns about doing this, including potential conflicts of interest in making private companies responsible for paying patients' Medicare benefits, including those attached to private insurance firms. The Department of Human Services' "corporate knowledge" of Medicare – which is not written anywhere, would also be done away with if payments were entirely outsourced.

Ms Faux, who is doing a PhD on Medicare compliance, said "the overriding issue is that Medicare is not something that can survive a corporate collapse".

On the 32nd anniversary of Medicare, Opposition leader Bill Shorten posted a television advertisement of Bob Hawke reminding Australians to sign up to it on social media. After this week's story broke, he tweeted: "First the Liberals tried to kill Medicare, now they're trying to sell it. Only Labor can be trusted with Medicare."

In the absence of policy, this political message is capable of again gathering its own momentum, this time ahead of an election.