Here is a bit of history from a country that has had a few referendum and plebiscites. Over 30 (I think, I'm being lazy) since 1901. Overwhelmingly, they have been necessary to amend the constitution (referendum) rather than votes on general public issues (plebiscite). Same sex marriage is not constitutionally required but is, unusually, a public vote on a general public issue where politicians don't want to make the decision. A plebiscite.
One third of referendum have succeeded. Generally, Australians are suspicious of change on big issues.
No (or very very few and none recent) referendum or plebiscite have succeeded without bi-partisan support from all major parties. This promotes consensus and unity.
All extreme proposals have failed miserably - military conscription in WW1, bank nationalization or outlawing the communist party.
Years are spent in developing Parliamentary committee reports, consultative committees, public debate on options etc before a refined question is put to the people. Same-sex marriage will be more a pig in a poke affair but it is not a constitutional amendment merely a plebiscite.
Our referendum are a bit different - to be successful you need a majority of overall votes and a majority of states. This can mean that small population states can defeat the day and. therefore, there is a greater need for consensus rather than winner (in terms of overall votes) takes all. (The UK is currently considering other aspects of our voting systems and how they promote consensus)
The overall approach in the last 50 years, in the case of successful votes, has been to first develop a national consensus and then put it to a vote (referendum or plebiscite) with the prospect of overwhelming support.
We face another referendum in the next few years over recognition of aboriginal people in the constitution. Years have been spent in developing a consensus and the terms of the question and this has been done to avoid ugly acrimony, misunderstanding and opportunities for racists to turn it into a brawl. The result has never been in doubt the only issues were the precise question and ways to ensure a dignified debate and an overwhelming result.
Why would you want to take an historic decision about the nation without overwhelming public support? How would that promote unity/ Oh I forgot you have the fail safe unity machine - the crown.

With that you don't need consensus.
I glamorize the Australian system only slightly and purely for tactical advantage.
An afterword. The Irish had to do a constitutional referendum on same sex marriage. It could not be done by Parliament. As it happened it was an overwhelming vote but only after a very ugly campaign where people who would not normally get a voice in sensible politics were given a forum to spit hate.I guess the lesson, understood in this country, is that these votes on single issues mean a whole lot of people come out from under stones and feel entitled to engage in irrational rant. Nothing wrong with old fashioned bigotry presented as a rational debate - but the Irish experience was of something worse.