There is a wealth of information on the topic. This topic typically elicits an emotional response, but I will try to give you some primary source statements and records on what happened:
"One of the things that troubles me," the First Lady confided to an overnight White House guest in the fall of 1941, "is that when people are in trouble, whether it's the dust bowl or the miners-whoever it is, and I see the need for help, the first people who come forward and try to offer help are the Jews. Now in these terrible days, when they need help, why don't they come? Or when they come why do they speak in a lower fashion?" Judge Justine Polier, a colleague in the Office of Civilian Defense and the daughter of American Jewish Congress president Stephen Wise, replied: "Mrs. Roosevelt, you have got to realize this is one of the consequences of the persecution and indifference of the so-called Christian world. Jews have come to feel that they have only to depend on themselves. This is the price Christianity has exacted."
Eleanor, however, is not her husband. The government was similarly not disposed to do anything prior to the outbreak of the war. From the same paper:
At Polier's request she enthusiastically - although privately- backed a Congressional resolution to admit 20,000 children beyond the German immigration quota during the next two years. The rising public temper of nativism, antisemitism and economic insecurity, combined with the presence of a more conservative Congress after the 1938 elections, convinced the administration to maintain official silence. Senator Robert Wagner, (D., N.Y.) with- drew his bill that June.^^1
That occurred in 1938. Again, though, what about her husband? We know he was silent then, what about later?
Well, Arthur Morse (While Six Million Died: A Chronicle of American Apathy) and Henry Feingold (The Politics of Rescue) both placed the majority of the blame at the feet of resistant State Department officials, according to the same paper cited as ^^2 . David Wyman (The Abandonment of the Jews: America and the Holocaust, 1941-1945) apparently reinforced this view, and criticized Roosevelt for being callous and not taking action during this time.^^2
What about Roosevelt's personal views? I did a little searching, to try and find some more documents on his beliefs, rather than just basing it on his inaction:
For the President, it was politically expedient to delegate refugee matters to the State Department and allow it to absorb criticism from those disenchanted by United States passivity.5 Roosevelt, in characteristic fashion, at once appeased restrictionists and maintained his benevolent image in the eyes of American liberals and Jews. Roosevelt might have responded more boldly to Nazi persecutions of Jews had there existed a political incentive. American Jews failed to provide one.^^3
It seems he simply didn't see incentive, and saw only political cost to himself. However, I was still unsatisfied with this answer in its completeness and proof, so I kept looking:
Morgenthau presented a special report to President Roosevelt on 16 January 1944. It was a damning indictment of State Department apathy and incompetence and ended by suggesting that 'the matter of rescuing Jews from extermination' be removed from 'the hands of men who are indifferent, callous and perhaps even hostile.' Morgenthau reminded the President that rumours of anti- semitism in the State Department 'will require little more in the way of proof for this suspicion to explode into a nasty scandal.' The warning impressed Roosevelt. The President sensed the political unfeasibility of continuing to delegate refugee matters to the State Department, particularly in 1944, an election year. He decided to heed Morgenthau's advice to form a government rescue commission. On 22 January 1944 the President issued Executive Order 9417 establishing the War Refugee Board and named Secretaries Morgenthau, Hull and War Secretary Henry Stimson to head the Board. Roosevelt gave broad powers to the WRB; it would formulate rescue plans, coordinate relief to the victims, find means of transportation to evacuate victims, and set up temporary refugee havens. Significantly, the WRB was authorized to negotiate with neutral countries to absorb refugees, either permanently or temporarily. Roosevelt appointed the energetic John W. Pehle as acting director of the Board. As Assistant Treasury Secretary, Pehle had helped unearth evidence of State Department procrastination on rescue efforts. Now he threw himself completely into rescue operations.^^4
However, this was very late, don't forget. Early 1944 was still a good amount into the war. However, up until this point, Roosevelt had refused to intervene in the State Department's control of refugee admittance to the United States, and had faced very little criticism over it. Only then did Morgenthau break through to Roosevelt, and only with pleas during an election year.
^^1 Eleanor Roosevelt and the Plight of World Jewry Monty N. Penkower Jewish Social Studies , Vol. 49, No. 2 (Spring, 1987) , pp. 125-136
^^2 America and the Holocaust Deborah E. Lipstadt Modern Judaism , Vol. 10, No. 3, Review of Developments in Modern Jewish Studies, Part 1 (Oct., 1990) , pp. 283-296
^^3 The Campaign for an American Response to the Nazi Holocaust, 1943-1945 Sarah E. Peck Journal of Contemporary History , Vol. 15, No. 2 (Apr., 1980) , pp. 367-400
^^4 Still Peck.