Same-sex marriage would comfortably become law if parliamentarians were granted a free vote – without the need for a plebiscite – analysis by marriage equality advocates shows.

But a stalemate looms if the Turnbull government's proposed plebiscite fails to pass the Senate, where it currently has the support of just 37 senators – two shy of the 39 needed.

The analysis found at least 84 lower house MPs and 41 senators in the new Parliament would vote in favour of marriage equality if a free vote were granted – enough to succeed in both chambers.

"Marriage equality enjoys clear majority support in both houses of Parliament," said long-time gay rights campaigner Rodney Croome. "If the Coalition allowed a free vote, marriage equality could pass tomorrow and the nation could move on."