In the early 1940s Walt Disney was developing a feature film based on Roald Dahl's book "Gremlin Lore", and asked the other studios to refrain from producing gremlin films. While most of the studios complied, Warner Bros. already had two cartoons too far into production--this cartoon and Russian Rhapsody (1944). As a compromise, Leon Schlesinger re-titled the cartoons to remove any reference to gremlins. The original title was "Bugs Bunny and the Gremlin". Ultimately, the Disney film was not produced or released.
In the opening scene, Bugs is reading a book titled "Victory Thru Hare Power". It's a spoof on the title of "Victory Through Air Power", by Maj. Alexander de Seversky, published by Garden City Books, NY, in 1942. It was also adapted into a documentary film produced by Disney and released in 1943.
At one point, Bugs says, "I'm only 3-1/2 years old." This is a reference to a popular catchphrase often uttered as a punchline by the character Little Audrey on the Bud Abbott and Lou Costello radio show, which started airing in 1942. The line was later frequently used in Looney Tunes and Merrie Melodies shorts.
As the heart of the scared Bugs Bunny is beating rapidly, it is visually marked as "4F". That is Army code for drastically limiting medical condition, hospitalization required, or ineligible to be inducted via the draft.
At one point the gremlin says to Bugs, "it ain't Wendell Willkie!" Wllkie was the Republican nominee in the 1940 US presidential election running against the incumbent Democrat in the White House, Franklin D. Roosevelt, who eventually won, becoming the President of the US for an unprecedented third time. Tragically, both Willkie and Roosevelt died soon after the 1944 election, which Roosevelt also won.