...Led by Hillel Kook (1913-2001), who used the pseudonym “Peter Bergson,” the group sponsored hundreds of full page newspaper ads, lobbied in Congress, and organized a march by 400 rabbis to the White House to plead for U.S. action to rescue Jews from the Nazis.
But the group also sparked its share of controversy. The Roosevelt administration, which resented the group’s pressure for rescue, used the FBI to spy on Bergson and tried to have him deported. Some mainstream Jewish leaders were also unhappy with Bergson. World Jewish Congress co-chair Nahum Goldmann told the State Department in 1944 that his colleague, Rabbi Stephen S. Wise, considered Bergson “as dangerous as Hitler” because Bergson’s activities might “cause pogroms” in the United States.
The fact that the Bergson Group made so many enemies may help explain why resentment against it lingered for so long, and why it was only recently that its activism has been gaining recognition and appreciation...
My Holocaust related views on FDR come mostly from Robert Rosen's "Saving the Jews, Franklin D. Roosevelt and the Holocaust".
For Churchill I use Martin Gilbert's "Churchill and the Jews, a Lifelong Friendship".
Both books defend the leaders, and cut them a lot of slack.
Their main point is that we have to remember the generally anti-Semitic context of that time.
So I can't judge whether either FDR or Churchill coulda or shoulda done more to help.