There were many reasons why Jews were not rescued in great numbers in World War II. American anti-Semitism (and fear of American anti-Semitism) was only one of many reasons. Others included:
1. fear that concentration on Jewish rescue would compromise the overall military objectives by compromising purely military priorities.
2. major disagreements amongst Jewish groups as to the form rescue activities should take, and as to where Jews should be moved.
3. fear that concentrating on moving Jews to Palestine would inflame Arab feelings, leading to Arab-Nazi pacts and elimination of western influence in the middle east.
4. fear that Jews moving to the United States would include spies planted by the Nazis.
5. fear that the continuing Depression would mean that the American economy could not absorb untrained newcomers.
And so on, and so on.
In retrospect, these may all seem wrongheaded, but they made sense (to varying degrees) to virtually everyone at the time.