Yes, if we're strictly talking about historical accuracy, Lindbergh's election is quite improbable (as depicted by Roth) for several reasons -- one of the chief ones being that to get Lindy to an electoral majority Roth has him breach the Solid South, which was not going to happen. There was plenty of anti-Semitism in the South, to be sure (indeed, in a lot of ways the Jim Crow South was the part of America that most resembled a fascist regime already), but the South was dominated by whites of English descent whose sentiments tended to be Anglophile. There's a reason that, as he steered the US into closer ties with Britain, FDR relied heavily on conservative Southern Democrats in Congress to back him in this course of action.
Lindy's base of support was German-Americans and other central European immigrant groups in the midwest.
While the camps existed in various forms already (geared more toward political prisoners at this point), the Final Solution hadn't really started until late 1940. Systematized killing really began with Operation Barbarossa (the invasion of the Soviet Union), involving mobile SS units; from there it ramped up through 1941 until the Wannsee Conference in January of 1942 formalized the plan for the death camps.
But as others noted, the general public wasn't aware of the Holocaust until the war was over and the advancing armies liberated the camps. There were rumours about this, but one of the problems that people trying to spread the word about the Holocaust encountered was that people were inclined to disbelief because of widespread propaganda about German atrocities during the First World War that had turned out not to be true.
