Maybe, but I would bet you that any poll question that contains the word "illegal" would get at least a 90% response.
"Do you oppose 'illegal' scuba diving?" "Do you oppose 'illegal' snipe hunting?" "Do you oppose 'illegal' food combining?
The fact is that most of us don't know who is legal or illegal, and have no way of distinguishing between behavior that is the result of immigration status and the result of lower income class.