If the Morrison government manages to get a referendum passed to give Australia’s Indigenous people constitutional recognition, it will be truly remarkable.

Prime Minister Scott Morrison has previously taken little interest in this area, at least publicly. And he would have done something that proved beyond Tony Abbott, for whom it was a cause.

Morrison and his minister for Indigenous Australians, Ken Wyatt, would have stared down conservative colleagues, cut a deal with Labor, and persuaded enough Indigenous leaders to get on board.

Finally, the government would have overcome the public’s inherent negativity towards referendums.

It would, one might say, be another miracle.

But miracles are rare and on present indications this one will be extraordinarily hard to land.

We are yet to see how seriously committed Morrison will be to the recognition push. For a chance of success, he’ll need to put his back into it.

Read more: The Morrison government proposes an Indigenous recognition referendum this term

His appointment of Wyatt, a man of Noongar, Wongi, and Yamatji heritage, was a statement in itself. The nomination of recognition for early attention was a surprise – and another indication that we have yet to get a grasp on Morrison as prime minister (as distinct from campaigner).

There has been much talk about his lack of an agenda, but the unveiling of a couple of significant priorities - industrial relations and now Indigenous recognition – suggests there might be more there than we suspected.

It’s important to be clear about what Wyatt – who outlined his proposals in a speech on Wednesday – is saying.

The government’s ambit hope is to put a referendum for recognition during this parliamentary term. But this will only happen if two conditions are met: it can get consensus on the content of what would go into the constitution, and there’s a high probability of a favourable outcome. The latter means winning not just the overall vote but the vote in four of the six states. Both content and potential support will present major problems.

What of the timetable? If the government really wants to give constitutional change a red hot go, there is a case for pushing it hard and quickly. Support doesn’t necessary build as time passes; beyond a certain point, it can erode.

But judging whether and when there would be sufficient likely public backing for a Yes vote would be tricky. Post May 18, everyone has become rather chary of polls. And things could quickly change in the final countdown.

History shows the voters’ penchant to say No. Despite the triumph of the 1967 referendum to give the federal government power to make laws for Aboriginal people and count them in the census (carried overwhelmingly in every state), referendums generally fail. Only eight have been passed - the last in 1977.

Read more: Listening with 'our ears and our eyes': Ken Wyatt's big promises on Indigenous affairs

Formulating the question will be an extremely challenging hurdle to climb over.

A constitutional change that acknowledged Australia’s First Peoples but didn’t go much beyond that would be easiest to get through government ranks and the popular vote.

It is hard to see either Indigenous leaders or Labor accepting just that.

Aboriginal and Torres Strait Islander leaders in their 2017 Uluru Statement from the Heart called for “the establishment of a First Nations voice enshrined in the constitution”.

But the indications are a voice would not be part of the government’s constitutional model. Wyatt does want a voice at the national level, but he is vague about its form, and the official line is that Morrison has “no plans” for the voice.

Labor was committed at the election to putting into the constitution a voice – which would be an input to the political process, not any sort of third chamber of Parliament – and the ALP would come under attack from Indigenous leaders if it walked away from this.

Writing for the Sydney Morning Herald on Thursday, Labor’s Pat Dodson, shadow assistant minister for reconciliation and constitutional recognition (and an Indigenous man dubbed “the father of reconciliation”) declared:

We either deliver the Uluru Statement from the Heart in full or continue down the failed path of soft reconciliation measures.

The shadow minister for Indigenous Australians, Linda Burney (also Indigenous), who is working closely with Wyatt and will do some travelling with him, may be more flexible than Dodson. Nevertheless she said after Wyatt’s speech:

We are at a point in our development, in our history where a voice to the parliament absolutely has to be entrenched in the Australian Constitution.

Morrison has had talks with Anthony Albanese to pursue bipartisanship on Indigenous issues and the Labor leader was optimistic on Thursday that a successful recognition referendum in the next three years was “absolutely realistic and doable”.

Read more: Constitutional reform made easy: how to achieve the Uluru statement and a First Nations voice

But former Deputy Prime Minister John Anderson, a member of the review panel Abbott set up to examine possible pathways to constitutional recognition, says that while he’s sympathetic to what Wyatt is undertaking,

finding the necessary national unity to avoid hurt and disappointment will be far from easy.

One huge problem, Anderson believes, will be getting Aboriginal people to come together on an agreed model.

Those in the Coalition party room and in the right wing commentariat who are critical of the move for recognition will use the spectre of the voice as a scare tactic.

The recognition issue will be one test of whether the right, though tamed since Malcolm Turnbull’s overthrow, will seriously arc up within the Liberal party in this term.

But Wyatt has attracted enthusiasm from some colleagues. NSW Liberal John Alexander was quick to declare

I’m with Ken on this, he has my full support for the process he has initiated and I hope it can conclude with a successful referendum vote and form of voice we can all be proud of.

Of particular importance, many big corporations, including mining companies, now have progressive positions on Indigenous affairs and will swing in behind the move. Wyatt has indicated he would be looking to them to help carry the debate, particularly in his home state of Western Australia, where a referendum would potentially be a hard sell.

He’d be encouraged by sentiments such as from Woodside, which said the company was

proud to give our support to this process as we continue to walk together with courage towards a reconciled Australia.

Read more: Politics with Michelle Grattan: Ken Wyatt on constitutional recognition for Indigenous Australians

As with same-sex marriage, indeed probably more so, the corporate world is talking up an important social issue and prodding the politicians to act.

If Morrison has to retreat on Indigenous recognition, it is unlikely to make a great amount of difference to him. It won’t affect the outcome of the next election.

For Wyatt the issue has quite another dimension. This is a fight for his people. The stakes are personal, and must feel frightening high.