It may allude to a straw (thin plant stalk) held up to see in what direction the wind blows: in this case, the metaphorical wind of group opinion.
straw poll (plural straw polls)
- (idiomatic) A survey of opinion which is unofficial, casual, or ad hoc.
- 2002: I don't think it was innocence that made me want to carry out a straw poll of women friends on the plausibility of this passage — James Meek in London Review of Books, Vol. 24 No. 22, 14 November 2002
unofficial survey of opinion