I am very troubled by this phrase -- it's almost an oxymoron. Science is not democratic, and scientists aren't anointed arbiters of facts.
Anyone can be a scientist simply by following the scientific method and collecting data in good faith; and a lone outsider with new data can challenge 100 years of "consensus". Obviously they are subject to challenges themselves, or if it's unlikely enough they might reasonably be ignored (e.g. a known charlatan saying they observed cold fusion).
Did this terminology start with the "scientific consensus" on anthropogenic climate change (which I do not dispute, by the way)? I think I understand why it was used in that debate, but I don't think it was a good precedent. Now it's being used to directly apply to policy ("growing scientific consensus on the failures of the global war on drugs").
Before long, it will be used directly in political debates to try to force some scientific organizations to choose a side. And then all credibility is lost.
Researching policies that require deep analysis of scientific (or other) data should be left to think tanks or something similar.