Illegal yet a Resident? (2)

The recent flood of immigrants that has been coming into the United States continues to flow. What should the United States do?
Hispanics on one hand should be allowed to stay. There are some who legitimately want to become Americans, who come over to learn and to work. Some also are fleeing dangerous situations in their own country.
On the other hand there are those who come over here to get rich quick. They work during the crop season and then go back to Mexico and retire, living in luxury. The Mexican president, Felipe Calderon approves of the actions of course, and is encouraging it. He says that the U.S. is being insensitive to the workers who are the bases of the economic and social structure of America. He says that deporting families who have American born children is detrimental to the family seeing as it divides it.
The only problem is that some illegal mothers come over just before they give birth. For example, if a pregnant Hispanic woman comes into the United States her baby automatically becomes an American citizen. She immediately files for all the assistance usually provided for needy pregnant mothers, and the U.S. gives it to her because her baby is a citizen. Yet American woman are allowed to have abortions because their babies, who aren’t born yet, aren't really human beings. Who’s paying for the health care? American citizens!
The Mexican President also doesn't think that it is fair for those who commit crimes here should be tried here. He says that they are Mexican citizens and that they should be tried by the Mexican laws. To be just and fair the individual should be tried by the laws of the country that they are in, not of the country that they belong to.
Personally I believe that if illegal immigrants really want to become U.S. citizens then they should be able to do so. Only they must become citizens. I also believe that if the individuals in question are fleeing from unjust persecution that they should be allowed to come, and to stay.