Labor senator Sam Dastyari has described the Government's moves to hold a public vote on same-sex marriage after the next election as "bullshit".

After a prolonged debate in the Coalition party room this week, a clear majority of Government MPs and senators voted to maintain the party's position against legalising same-sex marriage.

The Prime Minister has suggested a public vote in the next term of parliament, but has not specified whether he favours a referendum or plebiscite.

If successful, the referendum option, which is backed by cabinet minister Scott Morrison, would lead to constitutional change.

"The type of issue that could be canvassed under Section 51 of the constitution — simply at the moment, in Clause 21, it just says 'marriage'," Mr Morrison said.

"You could equally put in there 'opposite- and 'same-sex marriage' and clarify very clearly what the meaning of the constitution is on this question, and to reflect [what] some would argue has been a societal change since the constitution was first written."

But Labor argues that given the difficulty of getting the double majority of state and national support required for constitutional change, the proposal is designed to fail.

Some conservatives and Christian groups that are opposed to gay marriage believe a failed referendum could push the issue off the national agenda for many years.

A plebiscite needs to reach a lower bar, only requiring national support, but the Government would not be not compelled to act on the result.

Speaking to reporters outside Parliament House this morning, Senator Dastyari said the Government's push for a public vote is designed to stop gay marriage being legalised.

"What we've seen happen on the issue of marriage equality in the past couple of days is disgraceful," Senator Dastyari said.

"It's a rort, it's a joke, it's a false premise and frankly we need to call it for what it is and that is bullshit.

"The Australian public have had their say, they want these laws passed, we can pass them now, frankly we should be passing them now."

Government MP Warren Entsch has been given approval for a private members bill to legalise gay marriage, but he has acknowledged the outcome of the party room vote this week suggests there would not be enough support in the Lower House even if Coalition MPs had a conscience vote.

Two Coalition backbenchers, WA senator Dean Smith and Queensland MP Wyatt Roy, have confirmed they are prepared to cross the floor on the issue.