This article talks about a study arguing that the easier it is to find cheap labor domestically, the less likely the jobs will be sent offshore. Immigrants, therefore, may be competing more will offshore workers than other workers in the U.S.
The study also argues that there may be a trend called in-shoring, where goods produced overseas, like Apple computers, help American businesses expand.
Overall, the authors of the study find no viable evidence of a connection between offshoring and the net creation of American jobs, and find that the problems with unemployment are "usually rooted in macroeconomic conditions, not in immigration or offshoring."
This article's author says that immigration not only increases jobs, but increases tax revenue, helps finance Social Security, and increases home owners and improves the business environment.