They knew, yes, they knew but they were not about to divert “War Effort” resources to save millions of Jews, besides FDR are and many centers of power in Washington, London and Paris didn't really care for the Jews anyway.
You stated:
...by not following up on and not supporting rescue plans which could have saved lives without compromising the war effort.
The FDR administration felt the exact opposite. Diverting resources to bomb concentration camps meant US/British bombers being shot down NOT on a mission to knock out the Schwienfurt Ball bearing factories but for “Humanitarian” purposes? Sorry to be so cynical but even today after the Holocaust nations follow their interests even if that means millions die.
No, even the British who could have opened Palestine for the flood of Jews appeased the Arabs (yes, Arabs, long before they decided to call themselves "Palestinians", read PLO).
Nobody wanted the Jews and the case is still the same only now, nobody wants the State of Israel to exist and flourish, which she does.
The Israelis take a good long look at what is happening all around them and they know, for not the Israel Defense Forces and American aid (which Obama gives reluctantly) they would be slaughtered in a way that is happening in Syria today.
You don't seem to grasp the fact that many of the proposed schemes to save some European Jews during the Holocaust period might not have involved Allied military resources at all, or not to any great extent. Some of them could have been implemented even before the start of WWII, like the admitting the St. Louis refugees or admitting some of the Czech children referred to in this thread. They were largely "private sector" operations, which could have benefited by just a bit of American government cooperation.
Again, I'd strongly recommend the book "While Six Million Died: A Chronicle of American Apathy," written by Arthur D. Morse and published c. 1967 which delves into a sad history that few are aware of.