Support for recognition of Australia’s first peoples in the constitution is below 60% in today’s Essential Report, with more than a quarter of voters uncertain about the issue and a solid core of people opposed, disproportionately conservative voters.

The result suggests there’s now a real question over successful passage of the referendum, which needs majority support in a majority of states: 58% of voters say they would vote recognition of Aboriginal and Torres Strait Islander, 15% say they would vote against it and 28% say they’re not sure.

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While Greens voters are very strongly in favour (76% support and 5% opposition) and Labor voters are also very supportive (67%-12%), Coalition voters are less enthusiastic: 52% support recognition but one-fifth oppose it and another 28% say they don’t know. And only 50% of “other” voters (non-Coalition/Labor/Greens voters) support recognition, while 23% oppose it. In the larger states, support among Queensland voters is lowest, at 55%; in NSW it’s 57% and in Victoria 61%.

A poll by Recognise in May found support for recognition at 63%, while opposition was at 12% and Don’t Knows at 25%, although according to Recognise more than half of Don’t Knows, when pressed, opted for support (Recognise’s overall figures were, accordingly, 77%-23%). While the 58% support in the Essential poll is still strong, the high “don’t know” response suggests there is fertile soil for opponents of recognition to cultivate opposition, particularly around spurious arguments about indigenous separatism or “race has no place”, an argument pushed by groups such as the Institute of Public Affairs that are anxious to avoid the appearance of overt bigotry.

The relatively weaker support among conservative voters also puts the onus on Coalition supporters of recognition, such as Tony Abbott, to more openly combat both internal opponents of recognition such as South Australian Senator Cory Bernardi and far-right Liberal-aligned groups like the IPA.

The result comes amid a surge of bigotry across the country in recent months, with a big rise in votes for extreme right-wing parties in the July 2 election, the racist One Nation party securing four Senate seats and an Essential poll last week finding nearly half of Australians support a ban on Muslim immigration.

Note: the results of the Recognise poll as reported in the original version of this article did not reflect that poll’s allocation of undecideds. The text has been corrected to note that the Recognise level of support that is comparable to the Essential result is 63%, not 77%.