The push for indigenous constitutional recognition is “doomed to fail” according to a possible leader of the campaign arguing against the change.

South Australian Senator Cory Bernardi, who’s conservative views include an opposition to halal certification, told the ABC he was suspicious of the overwhelming support for recognition in polls because no plans have been put forward.

“But when the details and the consequences are put in front of you, I think most people are conservative and say, ‘Do I really want to go down that path?’,” he said.

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“Virtually no-one is talking about this. Like most of Australia, this is a fifth-order issue at best,” he said.

Social justice commissioner Mick Gooda says Indigenous recognition is in danger of falling off the radar.

“I think it is something that has the potential to really divide Australians and I don’t see that there’s much merit spending time speaking about it until they actually put forward a proposal, and then we can have a credible discussion about the consequences of what they put forward.”

Senator Bernardi said he would consider advocating for the No campaign against recognition.

“If I think the consequences of what’s put forward are going to be bad for Australia, if they are going to divide Australians and categorise us by race, I would be absolutely campaigning for the No vote,” he said.

The push for indigenous recognition is at risk of falling off the radar, said Aboriginal and Torres Strait Islander Social Justice Commissioner Mick Gooda.

“What we need urgently to happen is that this thing starts moving about engagement with the Aboriginal leaders at the top level of Government and the Opposition,” he told ABC 7.30.

“If we don’t hurry up and move on … we’ll get caught in a state of drift where nothing will happen and the whole thing will fall from the public consciousness.

He said constitutional recognition would have practical outcomes for Australia.

“It would change the relationship fundamentally between Aboriginal and Torres Strait Islander people and the rest of the population,” he said.

A parliamentary committee on indigenous recognition will report on the best way to hold a referendum by the end of the month.