The Australian Electoral Survey is excellent. Ian McAllister and Sarah Cameron have recently authored a report on political opinion trends from 1987 to 2013 using electoral survey data.
Here are a few graphs highlighting public opinion on immigration and asylum matters within that time period. They tell an interesting story of both relative stability and change in opinion.
The first table is ‘which party best represents your view on immigration’ and the others are self-explanatory:
From the author’s website:
“Interpreting political opinion polls is sometimes difficult. On particular issues or with regard to particular personalities, opinions may change significantly in a short period of time as a result of an event or a changed circumstance. Small changes in question wordings or in sample design may cause what appear to be significant changes in public opinion when such changes are, in fact, an artefact of the survey’s methodology. The most reliable way in which to monitor trends in public opinion is to examine responses over an extended period of time, using questions asked in the same way and included in surveys that use the same methodology.”