Liberal MPs are preparing to land a formal position on an Indigenous voice to parliament after spending months trading barbs with Labor over the proposal.
Opposition Leader Peter Dutton has summoned party members to a meeting in Canberra on Wednesday.
Ahead of the meeting, former Liberal voters in "teal" electorates are being urged to hit the phones in support of the voice.
Some elected Liberals are calling for a conscience vote, with NSW senator Andrew Bragg and Victoria's Jason Wood saying that is in line with party tradition.
Senator Bragg, who has indicated support for the voice, wants the party to follow a precedent set during the republic and marriage equality debates, when MPs were not bound by one position.
Former minister Ken Wyatt, the first Indigenous person to be elected to the House of Representatives, has also called on the Liberal Party to allow a conscience vote, saying he expects many to back the 'yes' campaign if given the chance.
In an address to the National Press Club this week, shadow attorney-general Julian Leeser questioned the timing of the proposal and urged the Albanese government to delay the referendum.
Mr Leeser also said it was possible the Liberals would not come to a "completely concluded" position.
The Yes 23 campaign, an independent group in favour of the referendum, is asking people who live in electorates represented by teal independents to contact Liberal MPs.
"Your community exemplifies what can happen when the voices of moderate Liberals and the Australians they represent are drowned out in the party," the group said.
"It would be very powerful if you as a former Liberal party constituent would get on the phone to ensure that your voice is heard by some key Liberals as they head into the party room discussion.
"If you have previously voted Liberal, tell them that and tell them why you changed your vote."
Meanwhile, a Newspoll conducted for The Australian and reported on Tuesday night shows 54 per cent of all voters support constitutional recognition and and the voice to parliament, with 38 per cent opposed.
The poll signals the likelihood that a referendum would meet the critical double majority test to succeed if one were held today, and that the referendum would also meet the requirement of obtaining a majority of voters in a majority of states, with Queensland the only state to fall short.