A public poll to determine whether we should have mandatory minimums? You have got to be kidding!
In order to better inform themselves  on this topic I recommend that the Minister,the Government and your readers, commentators and reporters read the Report of the Canadian Sentencing Commission "Sentencing Reform A Canadian Approach" from February 1987 and in particular Chapters 8 on "Mandatory Minimum Penalties" that recommends their abolition except for murder and high treason, and Chapter 4 "Public Knowledge of Sentencing" that explains how people naturally get most of their information from a 10 second clip on TV or a few paragraphs in a newspaper about some unusual and exceptional case and emotionally gut react to these stories before putting their brains in gear and politicians react accordingly!
This is not to blame the Media as they would go broke reporting the routine mundane cases our Judges see daily and are simply supplying a demand from the public for titillating stories.