For a variety of reasons Hitler calculated that war with the US would in fact be in Germany's self interest. This is evidenced by the fact that Germany declared war on the United States in the wake of Pearl Harbor (on Dec. 11th ), not the other way around. Hitler believed that this act would compel the Japanese to attack the Soviet Union in turn, which would open another front in the East. This was a grave miscalculation as Japan did not do so.

Furthermore, there wasn't even a real obligation for Germany to declare war on the US after Pearl Harbor- the Tripartite Pact was in truth a non-aggression and defense pact, meant to draw in its signatories only when one was attacked. It was not truly an alliance (in a technical sense) which meant Japan had been free to remain at peace with Russia post Barbarossa until the Russians declared war on them in 1945.