I'm aware that people in the US government knew, fairly early on (1942, as I hazily recall) that the Nazis were embarking on a program to exterminate the Jews in Europe. When did the American public find out? My perception is that the people in the US didn't realize the full extent of the Holocaust until after VE Day, when news of what had actually gone on in the camps started to emerge from newly liberated German territory. Am I incorrect in this belief? Were there efforts to make Americans aware of what was happening to the Jews in Europe prior to the end of the war? And, if so, how successful were those efforts?
The first public media reports on the extermination of the Jews came out in November 1942, only a couple months after the US government had become aware of the existence of the extermination camps. These stories were picked up by papers around the country and the information about the ongoing mass murder of the Jews became widespread public knowledge.
The initial reports, which came from the head of the World Jewish Congress, Rabbi Stephen Wise, indicated that 2,000,000 Jews had already been killed and the Germans had plans to kill 4,000,000 more, which of course adds up to 6,000,000, roughly the number of Jews who were ultimately killed during the Holocaust. The number of Jews that had been killed up to that point was significantly underestimated, mainly because the initial reports came from Polish sources and therefore focused on the extermination camps in Poland, while the large-scale massacres of Jews during the invasion of the Soviet Union weren't as well-known (the Germans had probably killed over 1,000,000 Jews in the occupied Soviet Union by the time of these reports).
A few weeks later, on 10 December, the Allied governments issued a statement known as the Joint Declaration by Members of the United Nations, which announced to the world that they had received
numerous reports from Europe that the German authorities...are now carrying into effect Hitler's oft-repeated intention to exterminate the Jewish people in Europe...Jews are being transported in conditions of appalling horror and brutality to Eastern Europe. In Poland, which has been made the principal Nazi slaughterhouse, the ghettos established by the German invader are being systematically emptied of all Jews except a few highly skilled workers required for war industries. None of those taken away are ever heard of again.
As we now know, the key elements of this statement were an accurate description of the ongoing Final Solution.
However, this statement and the public reaction to the ongoing reports about the Holocaust didn't immediately prompt the US government to act, nor did further reports from eyewitnesses like Jan Karski. The State Department actually censored some reports about the Holocaust even though the public already knew about it because they wanted to avoid public pressure to take further actions (e.g. admitting more refugees). These actions reflect the lack of agreement in the US government about what, if anything, should be done to mitigate the mass murder of the Jews. Finally, in January 1944, the War Refugee Board was established to provide relief to refugees from Nazi-occupied Europe, by which point the extermination of the Jews of Poland was largely complete.
If you want to see primary documents and media reports from the time, I highly recommend you check out the USHMM's Americans and the Holocaust exhibition, which goes into great detail on public awareness and public opinion regarding Nazi Jewish policy and included a large-scale citizen science project to collect stories about the Holocaust from local newspapers throughout the US.