"Politicians should do their job. This could be the last chance to save taxpayers $160 million [on a plebiscite]. It will also avoid a needless extended acrimonious debate," Leyonhjelm said in a statement.

Leyonhjelm announced he will move to re-introduce a 2013 bill from Greens senator Sarah Hanson-Young, the Marriage Equality Amendment Bill 2013 . Leyonhjelm claimed he had secured support for Hanson-Young's bill from Labor and crossbench senators. The bill would define marriage as "a union between two people," rather than "between a man and woman" as in current legislation.

Liberal Democrats Senator David Leyonhjelm says he will seek to re-introduce a bill to legislate marriage equality to the Senate this week, which is expected to pass by marriage equality advocates.

Senator Sarah Hanson-Young

The Senate would need to vote to allow the bill to come for debate, then vote on the bill itself. Australian Marriage Equality National Director Rodney Croome believes such a bill would pass the Senate. His organisation keeps tabs on public and private comments made by politicians on marriage equality, and believes there are enough supporters to pass the legislation.

"There are two different figures. The publicly declared, that is a slim majority of around 41 senators (out of 76) but the number would probably be larger as there are some senators who have told us they will vote for it but haven't said so publicly. With a free vote, there would be a majority, without any doubt, based on public supporters," he told The Huffington Post Australia.

If the bill passes the Senate, marriage equality would not become law; it would need to also be introduced to and passed by the House of Representatives to come into force. While the Coalition and Turnbull have continually pushed their support for a plebiscite on marriage equality, it seems unlikely that a marriage equality bill would be allowed to come up for debate in the House -- indeed, the government shut down Labor MP Terri Butler's recent attempt to reintroduce marriage equality legislation.

However, Croome said he believed the passage through the senate of a marriage equality bill -- as well as Monday's news that a plebiscite could cost in excess of $525 million -- may encourage the government to consider allowing marriage equality legislation to be debated in the House.

"If a marriage equality bill passes the Senate, it will be a huge step forward. It will send a message to the government and the public that we don't need a plebiscite, that it can be resolved in parliament, and it would be a huge morale boost for equality supporters after years of campaigning," he said.

"It would increase pressure on the government for it to be debated and passed in the lower house. I think we have a majority of support in the House as well as the Senate."

Hanson-Young's bill was introduced in December 2013, but sat idle for almost two years before a second reading debate in November 2015.

HuffPost Australia has contacted Hanson-Young's office for comment.