The survey was conducted last week, covering 700 respondents, and the findings were published by Dnevnik daily on Monday.
Bratusek's Positive Slovenia party would receive 8% of the vote in a new election.
Support for the government and the leading parties declined mildly from last month.
The number of Slovenians who do not know for which party they would vote or would not go to the polls rose from 46 to 51%.