Less than half of Australians want a plebiscite on same-sex marriage, a poll has found, with support for a national vote plummeting once voters are aware that the Turnbull Government's proposal will cost $160 million but not compel members of Parliament to respect the result.

Support for a plebiscite appears to have softened since it became a battleground issue during the election, with Opposition Leader Bill Shorten mocking it as a "$160 million taxpayer-funded opinion poll".

A Galaxy poll of 1000 people taken from Thursday to Sunday this week found 48 per cent support holding a plebiscite to determine whether same-sex couples should be extended the same marriage rights as heterosexual couples.

That outweighs the 30 per cent who oppose a plebiscite but the result is significantly lower than a July 2 Fairfax-Ipsos poll of nearly 1400 voters that found 69 per cent of people backed a nationwide vote over a vote on the floor of Parliament.