Coalition backbencher Warren Entsch's same-sex marriage bill will be introduced to Federal Parliament Monday morning as Cabinet prepares to discuss the timing of a popular vote on the issue.

It was Mr Entsch's strong stance on same-sex marriage that set in train last week's marathon Coalition party room debate on allowing a conscience vote.

His bill now looks likely to make just a single appearance in Parliament, before it is sent off to a parliamentary committee along with other private members' business.

About two-thirds of the Coalition party room opted to support the status quo — that marriage is between a man and a woman, and it should be the nation that decides whether to allow the change to the Marriage Act.

Prime Minister Tony Abbott wants a constitutional referendum, or a non-binding plebiscite, to be held after the next federal election, expected within about a year, and he appears to have made up his mind on the timing.

"The fundamental decision is that this Government in the next term of parliament will put this very important question to the people for their decision," Mr Abbott said on Sunday.

Mr Entsch said he did not support a referendum and wanted the Coalition to commit to a people's vote within 100 days of the next Parliament.

"If the vote comes up and I'm asked to vote of course I will support it," he said.

"There would be no purpose in introducing it into the Parliament if I'm not prepared to stand by what I've introduced.

"I introduce it because I would like to get these stories out there, a little bit of background on this. I don't introduce it with an expectation that it's going to be successful."

Mr Entsch also said members should not lead any campaigns either for or against same-sex marriage.

"I think it would be grossly inappropriate for members to say we have established that it's not for us to make a decision, it's for the people, and then for them to lead campaigns one way or the other," he said.

"I will be very strongly critical of any colleagues that go out there publicly and try and lead campaigns one way or the other."

The issue is set to be discussed when Cabinet meets late Monday afternoon, with Communications Minister Malcolm Turnbull on a collision course with Mr Abbott.

Mr Turnbull, a supporter of legalising gay marriage, argues a plebiscite should be held before the next election so the issue does not distract from the Government's core messages.

"The Prime Minister has indicated a disposition to have this considered after the next election," Mr Turnbull wrote on his blog on Sunday.

"The party room has not debated the matter, nor indeed has the Cabinet."

Attorney-General George Brandis was not sure about holding a vote before the next election.

"A referendum or a plebiscite costs an enormous amount of money," Senator Brandis told Sky News.

"The public would be a little weary of being taken to the ballot box twice in 12 months."

However, Senator Brandis agrees with Mr Turnbull that a plebiscite would be better than a referendum to change the constitution, a course favoured by Social Services Minister Scott Morrison, an opponent of same-sex marriage.

He said a date for a national poll on the issue needed to be decided "very soon".

His call came as thousands of people around Australia rallied in favour of marriage equality over the weekend.