I think that depends on the state. Some states have many people focused on illegal presence. And to the extent the public gets restive for work, and sees illegals getting work and benefits, the public will come to associate "bad economic times" with "presence of illegals."
Texas has spent $230 million in recent years to secure and police the border with Mexico.
Can someone give me a dollar amount that Texas or Governor Perry should spend to convince naysayers that he believes illegal immigration is a serious problem?