Do the Parties Really Agree on Emigration Reform?

In the nineties, republicans and democrats basically agreed about how good emigration was like. Doesn't that suggest that the parties, or maybe the media, caused a shift in public opinion rather than the other way around? I am very sceptical of public opinion polling on to issues that are not at the centre of public opinion. When it actually became an issue, the parties did polarize. So i think they polarized in a predictable way, given what the underlying coalitions were.