The debate over changing the definition of marriage to include Australians in same-sex relationships has struck a political impasse.

Attorney-General George Brandis — himself a supporter of change — has pleaded with Labor leader Bill Shorten to allow the Government to go ahead with its plebiscite.

Talks between the Attorney-General and his Labor counterpart Mark Dreyfus failed to agree to anything — with Labor still on track to make a formal decision in a fortnight to block the Government's plans to hold a plebiscite in February.

Coalition MP George Christensen, who is opposed to same-sex marriage, tweeted after the meeting that "the definition of marriage won't be changed for the foreseeable future — thanks".

Senator Brandis responded on 7.30.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 6 minutes 15 seconds 6 m George Brandis discusses same-sex marriage plebiscite meeting

"Mr Christensen's tweet makes the point I have been making, [which] is that what Bill Shorten is doing by playing politics with this issue is playing himself and the Labor Party right into the hands of people who do not want to see marriage equality," he said.

"As a supporter of marriage equality, I think that's a great shame. The only person standing in the way is Bill Shorten.

"I renew my plea to Mr Shorten: stop playing politics with the lives of gay people."

'What is that preparedness to compromise?'

But Mr Dreyfus says the Coalition would need to go much further to win Labor's support.

"It might be that as George Brandis was urging on me in the meeting yesterday that I shouldn't listen to the Deputy Prime Minister when he says there's to be no change," he said.

"I should apparently listen to the suggestion made by the Prime Minister that there is a preparedness to compromise — well what is that preparedness to compromise?"

The Opposition has been calling for the Government to drop public funding for both sides of the debate, and wants same-sex marriage to be legalised automatically if the public votes yes in the national vote.

But Mr Dreyfus said those two changes would not be enough to secure Labor's vote.

"The Government needs to go a lot further than that," he said.

"The problem that has occurred here is that the Government is not even suggesting that it is prepared to actually change."

Plebiscite a divisive issue

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In the Q&A audience on Monday night, David Hunter put the issue to Labor frontbencher Penny Wong.

Ms Wong responded by saying that Labor wanted a "free vote of MPs in the Parliament" rather than a plebiscite.

"Some Coalition MPs who oppose same-sex marriage, like Tony Abbott, have said if a plebiscite is held and carried they'd then vote for it when the result came to the Parliament for endorsement," she said.

"Others have said they couldn't do that."

David Littleproud who holds the regional Queensland seat of Maranoa for the LNP is in that camp. He spoke to Lateline.

"I'm here to represent the people of Maranoa. They send me down there to go in to vote for them," Mr Littleproud said.

"Their views are just as precious as anybody else's and they should be respected and they should be given a voice."

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 11 minutes 11 m Debate: Maranoa MP David Littleproud and Tiernan Brady

Tiernan Brady campaigned for change in Ireland, and has now joined Australians for Marriage Equality.

On Lateline he expressed his dismay at the direction this debate was taking.

"Nobody's talking about marriage equality anymore, we're talking about political process and political parties," Mr Brady said.

"And we're missing what this is about which is about lesbian and gay people who are in almost every family — the people who live on our street, the people we work with."