Illegal immigration has impacted American thinking on immigration mostly in negative ways. That is, Americans have become somewhat less inclined to support immigration in general as they have come to associate immigration with illegal immigration. Illegal immigration has also lessened the demand for legal immigration.
First, the huge numbers of illegal immigrants in the country make there be less need for legal immigrants. If there were no illegal immigrants, there would be room for many more legal immigrants. Those legal immigrants would be needed to fill jobs now held by illegals. This means that illegal immigration has reduced our need for legal immigrants.
Second, and perhaps more importantly, illegal immigration has caused many Americans to have more negative attitudes towards immigrants overall. The presence of a large number of illegal immigrants has caused many Americans to worry about the impacts of immigration on our society. They feel that these immigrants will overwhelm American society and change it in ways that are not palatable to them. Because they fear for the continuity of American society, they come to have more negative attitudes towards immigration in general.
Thus, illegal immigration has made American attitudes towards immigration more negative and has decreased the demand for legal immigration.