Australia is awaiting the results of its same-sex marriage survey, with Yes activists said to be ‘nervously optimistic’, after latest polling suggested a majority for those supporting marriage for same-sex couples.

Turnout for the voluntary $122 million postal survey is estimated at close to 80%, having taken place over a period of two months.

Prime Minister Malcolm Turnbull has returned to Australia following a regional conference for the result and is expected to face a difficult test to his leadership, amid divisions in the Coalition over legislation which would enact same-sex marriage.

In the event of a yes vote, a debate on legalising same-sex marriage could start as early as this afternoon, with two bills on the table. One of them, proposed by conservative senator James Paterson would allow religious ministers to refuse to officiate same-sex weddings, allow discussion of the traditional view of marriage without legal penalty, and allow parents to withdraw their children from classes that don’t reflect their view of marriage.

However, Prime Minister Turnbull has said Paterson’s bill has “virtually no prospect” of passing. He has previously hinted that legislation to allow same-sex marriage could be passed by Christmas following a Yes vote.

No campaigners, anticipating a vote in favour of same-sex marriage, have called on the government to not ‘bully [opponents] into silence’ and to respect freedom of religion and freedom of speech in its implementation.

Results of the survey are expected at 10am Canberra time (2300GMT).

The campaign was mired by homophobic and transphobic abuse, falsehood around LGBTQ+ rights and incidents of vandalism on both sides, with the No campaign claiming that same-sex marriage would harm children and reports of trains in Sydney being vandalised with swastikas encouraging No votes. A man was also charged with assaulting the godson of former Prime Minister Kevin Rudd following an argument about marriage equality.