If the same-sex marriage plebiscite is blocked, most voters, including many Coalition voters, want a parliamentary vote to determine the matter, this week's Essential Report suggests.

With the government's proposed plebiscite bill looking likely to fail in the Senate, 53% of voters say there should be a vote in Parliament if the bill is blocked, while 29% say there should not be. Greens and Labor voters strongly support a parliamentary vote, but more Coalition voters -- 46% -- support a parliamentary vote than oppose one -- 38%. Even "other" voters (voters other than Labor, Coalition and Greens), who tend to be socially conservative, support a vote, 53%-32%.