I apologize for the length of this answer; but I am disinclined to answer a serious question with a list of internet sites. The topic about which you ask deserves better.
Prior to and during WWII, the policies of the U.S. regarding Jewish refugees who were fleeing Nazi persecution and genocide were restrictive. Indeed, these restrictions are often referred to as the "Jewish Refugee Crisis." The Crisis that was at its worst from 1938 to 1944.
Through the quota system, immigration regulations, visa requirements, and the time required to process visa applications, the number of Jewish refugees, particularly those from Germany and Austria, was limited and then reduced. The U.S. failed to provide adequate safe harbor to Jewish refugees fleeing the persecution of Nazi Germany. The U.S. is a good and compassionate country; but it is a terrible truth that the U.S. turned away thousands of refugees, delivering many to their deaths at the hands of the Nazi regime. [I should hasten to add that other nations, particularly Russia, did little more to provide protection for the refugees.]
American politicians and bureaucrats, while maintaining an appearance of great humanitarianism, used immigration policies to prevent Europe's Jews from escaping to the United States. For example, the policy of the U.S. State Department was, at best, wrongheaded. Many Americans expressed concern that Germans posing as Jewish refugees were trying to establish themselves in the U.S. for a takeover. The State Department, particularly Breckinridge Long, Assistant Secretary, took these exaggerated thoughts and used them to cut their quotas in half again. He did keep the President informed of his policies, but he always stressed it was for the betterment of America. At one point he instructed the immigration consuls to place "obstacles" in the way in order to make it very difficult to gain a visa.
A.D. Morse writes: "In 1938 the Nazis burned every synagogue in the nation, shattered the windows of every Jewish establishment, hauled twenty-five thousand innocent people to concentration camps, and forced the Jews to pay 1,000,000,000 marks for the damage."... "Five days later, at a White House press conference, a reporter asked the President 'Would you recommend a relaxation of our immigration restrictions so that the Jewish refugees could be received in this country?' 'This is not in contemplation,' replied the President. 'We have the quota system'."
THE UNDERLYING REASONS FOR THE CLOSED-DOOR:
UNEMPLOYMENT -- In the early 1930’s there was a steady rise in unemployment in the U.S. Due to the onset of the depression it was difficult for a American to find employment, it was even more difficult for a newcomer to find employment here as well. Due to the depression, the Hoover administration tried to keep immigration entry down by using the interpretation of the Immigration Act of 1917 to keep aliens out who might pose a threat to government funds by being unable to find a job and supply money for themselves. The Roosevelt administration tried to follow the same guidelines but as the crisis in Germany increased there were a rise in immigration cases in the US. In 1935, President Roosevelt urged that the restrictions be eased due to the worsening conditions for Jews and others in the Reich. Unfortunately, the great increase of Nazi oppression occurred at the same time as the worst phase of the “Roosevelt Recession” occurred in the U.S. and unemployment rates were increasing rapidly.
"AMERICANISM"-- The twisted idea of "Americanism," is described briefly above in connection with the U.S. State Department. Ironically, many of the generations during this time were only first or second generation Americans. They, immigrants themselves in the few years past, were claiming "America was for Americans." Many wanted to conserve American resources for the Americans. They feared these immigrants and the intent that they might have coming to America. Many also feared the threat of their culture. Immigrants brought in new ideas and new cultural changes. Many feared how this would affect the upbringing of their children and the future of America, socially.
ANTI-SEMEMITISM -- The idea that “foreigners” were coming to America, fueled the anti-sematic ideas that already existed in the U.S. In a country where jobs were scarce and money was even harder to find, the idea of more immigration was hard to comprehend. The ideas of hate reached a peak in late 1930’s and early 40’s. The Jews were seen by some as an undesirable race. There was the argument that the Jews were behind a huge world-wide conspiracy of communism. Although much of America did not accept all of these ideas as complete truth, many of the ideas took hold and anti-semitism rose to new heights in the U.S.
1944 AND LATER:
It was not until 1944 that the U.S. began to take steps toward easing resrtrictions.