Attorney-General George Brandis and Special Minister of State Scott Ryan will meet with shadow attorney-general Mark Dreyfus in a last-ditch attempt to find a compromise that might win Labor's crucial support in the Senate. It precedes a cabinet meeting in Canberra on Monday night.

But any genuine attempt at negotiation appears doomed from the start, with Labor making demands to which the Coalition will find it impossible to accede.

Mr Dreyfus on Friday mentioned two changes - dumping public funding for both sides' campaigns, and making the plebiscite self-executing or binding - as necessary but not sufficient for Labor to reconsider its position on the issue.

"It needs to be cheaper," he told ABC radio. "We made it clear right from the outset that we opposed public funding."

Mr Dreyfus also said the self-executing option, whereby marriage equality would automatically become law if the plebiscite passes without the need for a subsequent parliamentary vote, was "an absolutely essential change".

But the government is unlikely to give ground on either point: self-execution would require a complicated legislative rethink and could raise constitutional concerns, while Coalition conservatives would not truck the removal of public funding.

"The first step is for the government to explain what changes to the plebiscite bill are acceptable to the right-wing of the Liberal Party," Mr Dreyfus told Fairfax Media. "Whether anything develops from that is entirely up to the government."

Government sources remained tight-lipped on Friday about what they might put on the table, but indicated Labor needed to accept the legitimacy of the plebiscite and the government's mandate.

Even if the meeting proves fruitless, it will allow both sides to argue they attempted to compromise, and blame each other for delaying same-sex marriage indefinitely.

Opposition Leader Bill Shorten said his idea of a compromise was to "just have a vote in the Parliament", but that Labor would "listen to all points of view in this debate".

Even if it wins concessions, Labor is still expected to oppose the plebiscite, which Mr Shorten has previously said could lead young LGBTI people to take their own lives.

It came as Labor seized on revelations Liberal Party members were behind an offensive and misleading flyer that claimed same-sex marriage would make the controversial Safe Schools program compulsory in local schools.

Labor's backing is crucial because the Greens and Nick Xenophon Team have already committed to voting down the plebiscite, and the Turnbull government does not have the numbers to get it through the Senate without Labor.

The opposition will adopt a final position at a caucus meeting on October 11.

The Greens accused Labor of "dragging its feet" on the issue and called on the party to walk away from negotiations.

"Labor must completely rule out a wasteful, divisive plebiscite," Greens LGBTI spokeswoman Janet Rice said.

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