Malcolm Turnbull faces a Nationals revolt over an ambitious plan for a body to provide indigenous oversight of law making.
A convention of Aboriginal and Torres Strait Islanders in central Australia last week recommended enshrining in the constitution an advisory body to give indigenous people a say on laws and policies that impact them.
Nationals leader Barnaby Joyce said while he accepted constitutional recognition, the proposed new body was self-defeating and placing in jeopardy any bipartisan support for the Uluru statement.
"(If you) ask for something that will not be supported by the Australian people, such as another chamber in politics or something that sits beside or above the Senate, that idea just won't fly," Mr Joyce told reporters in Canberra on Monday.
The deputy prime minister said the final plan needed to be something the government could "sell to the Australian people".
Cape York Institute senior adviser Shirleen Morris said there was no suggestion of a third chamber of parliament.
"All it is, is a constitutional mechanism guaranteeing that indigenous people can have a say, can give advice on laws and policies that are made about them," she said.
Nationals MP George Christensen said he would vote against the referendum bill in parliament if it proposed a new representative body.
"If they want to have recognition of the first peoples in the constitution in a preamble or a way that recognises them as the first people of the nation, so be it," he told Sky News.
"But this is dangerous to democracy if we start giving one group special privileges."
A Referendum Council leader is urging politicians to wait for its final recommendations on how best to recognise indigenous people before speculating on the prospects of success.
Co-chairman Mark Leibler said a report from its indigenous steering committee, due in the next few days, would add to the Uluru statement.
"Obviously, the Referendum Council is not going to recommend any particular referendum which is opposed by our Aboriginal and Torres Strait Islander people," Mr Leibler said.
Federal Labor frontbencher Linda Burney, a Wiradjuri woman, said the Uluru proposals were all "very possible" and the task now was to see how they could be applied.
She noted the statement was silent on constitutional recognition, which she saw as an important change, and scrapping the constitutional race power.
"I would advocate strongly that we do have to deal with the race powers because if we don't do that it could actually still give the parliament the capacity to do away with a body of any sort within the constitution," she said.
Ken Wyatt, the first federal indigenous minister, is confident the council's work on top of six years of discussion will lead to a referendum in 2018.
Greens MP Adam Bandt said when it came to a referendum, the parliament was probably more conservative than the Australian population.
"It's time for a treaty in Australia," he said.