I live in Winnipeg, home of the Human Rights Museum. There is an area that displays events when , in the past, Canada blocked refugees from entering, for example  Sihks and Jewish people. It also displays events about successful refugee events, such as the Hungarians and Vietnamese.  This has given me a different perspective. 
I remember when thirty  years ago, a young Asian woman asked me if I thought Canada was a "white" country. I myself was pretty young at the time. I answered that I wasn't really sure.  Thirty years later I would answer that it doesn't really matter. 
If you have a poll that essentially asks your opinion on an event that can be construed to lower your standard of living,  most people will probably answer  negatively. Furthermore, these border events are a symptom of  problems that must be addressed; world population, resource mismanagement and environmental degradation.  
A wise man once told be, " Do not be unnecessarily terrified".  Just necessarily so.