The "Little Man From the Draft Board" was based upon the famous radio character of Mr. Peavey, a supporting character on "The Great Gildersleeve" played by 'Richard LeGrand (I)'. His famous catchphrase was, "I wouldn't say that."
Although the headlines of victory in Europe were everywhere, the U.S. was still drafting troops for a planned invasion of Japan. The land assault was expected to take several more years and high casualties were expected. Fortunately, things turned out differently.
"Is this trip really necessary?" was a wartime phrase seen in cartoons of this era. It was advice to U.S. citizens to make only needed trips, thus saving already rationed gasoline, or providing transport seats for serving troops.
Daffy pays tribute to both Teddy Roosevelt (a bit tongue in cheek) and Douglas MacArthur before receiving his draft notice.
Daffy's supersonic like travels are illustrated with futuristic visual effects. Audiences would have appreciated this, as most comic book super heroes were involved in the war effort.