I dealt with this very controversy in my film, Who Shall Live and Who Shall Die?
. The explanation came from Josiah Dubois, a Treasury official who served with the War Refugee Board actually rescuing Jews-- who then went on to prosecute Nazi war criminals at the Nuremberg trials. As Dubois noted in his memorandum to Secretary Morgenthau on the acquienscence of the US government in the extermination of the Jews, one reason that steps were not taken to rescue Jews from Hitler was oppostion from the British government, an important American ally. To appease Arab public opinion, the British had persuaded the US government not to rescue European Jewry, using a variety of excuses. For, as the mandatory power in Palestine, the British were concerned that if Jews were rescued, they might go to their historic Jewish homeland, despite the 1939 White Paper restricting immigration . So, British foreign policy objectives required trapped European Jews to die, rather than be able to move to Israel. By the time American protests led to the formation of the War Refugee Board in 1944, it was too late--the vast majority of Jews had already been killed. After the war, surviving Jews did manage to immigrate to Palestine in violation of the White Paper...so, Israel was born. When Israel declared independence, it received arms from the US and Russia. Meanwhile, Britain supported Glubb Pasha's Arab army's attempt to drive the Jews into the sea. (This political configuration changed by 1956).
More on this subject at the Wikipedia Auschwitz bombing debate page...