Being an immigrant myself (legal, of course :) , my opinion is different from those who are born here. When true reasons( for their visit ) are given people face many problems to get the visa that makes it harder even to visit America . This is one of the reasons that illegal population has increased.
If people from neighbouring countries get work permit or work visa easily the situation of illegal immigration might be under control. Government officials know that these illegal immigrants are the cheap labors. If they are controlled, things will be different. However, if nation's broken immigration system is reformed it can be under control.
Not everyone has a hard life like Delfino or like Andres, but if the guest worker proposal supported by George W. bush is reformed , people like Delfino would not have any problem to immigrate to America.