People come here because they are fleeing hunger, violence, and an inability to provide for their families.  The reason that many of them cannot regularize their status, as people were able to do in the past, is because we live under a mean-spirited and counter-productive law that was passed in 1996.  We could easily change this law to make it possible for those who contribute to the economy and who do not break laws to regularize their status, so that they will no longer be without it.  
If we had a rational, humane immigration law, then we would, once again, experience something that is called "circular migration, ie people coming here to work for a number of years and then returning to their home countries, able to buy land or start a business with the money that they made here.  This improves the economies of the home countries, which, in turn, reduces the need for economic migration.  There is, of course, more to it, but this would be a start.