There are three main reasons for this.
First, the United States did not know that the Holocaust was going to happen before WWII started. When the US turned away refugees from Nazi Germany in the 1930s, it did not know it was condemning them to death.
Second, once the US found out about the Final Solution, there was very little that could be done about it. By this time, the US was at war with Germany. They could put no diplomatic pressure on Germany to stop killing Jews and there was little they could do militarily to prevent the Holocaust from continuing.
Third, we cannot ignore the fact that there was antisemitism in America at the time. This certainly played a role in causing the US to refuse to take refugees from Nazi Germany before the war.
Another reason is that, during WWI, American newspapers reported stories about German war atrocities that turned out to be untrue. So, when reporters from those same papers and other intellectuals and politicians heard about "death camps" in WWII Nazi Germany, they were very suspect. They had been burned before by false reports, so they were reluctant to believe and publish the new and (as it so terribly turned out) completely true accounts of Nazi concentration camps. I'm not excusing the American delay to get involved, just explaining it.