Well, Hitler certainly simplified things by declaring war on the US a few days after Pearl Harbor. I understand that under Nazi Germany’s treaty with Imperial Japan he was not obligated to do so.
What would have been ‘interesting’ would have been how FDR would have handled the situation had Hitler done NOTHING.
But FDR tells the Congressional leadership which came to the White House the night after the Pearl Harbor attack, that (to paraphrase) " ... we have it on good authority that Germany will declare war on us."
Not only FDR, but WSC also knows this - the British having three PURPLE analogues by that time in 1941. Odd, that the Asiatic Fleet had a PURPLE but the Pacific Fleet did not.
That "authority" was a PURPLE message from late November 1941, Berlin to Tokyo, reporting on a meeting with von Ribbentrop.