Disney Studio
Babbitt began his career at Disney as an assistant animator, but his talent was spotted and he was soon promoted to animator. His first important work was a drunken mouse in the short The Country Cousin (1936), which won an Academy Award for the studio.
At the Disney Studio, Babbitt animated the Wicked Queen in Snow White and the Seven Dwarfs, a job described by Disney animator Andreas Deja as "one of the toughest assignments" on the film. While he was working on Snow White, he met his first wife, Marjorie Belcher, a dance model whose live-action performance was used as reference material by the animators for the role of Snow White.
On the film Pinocchio, Babbitt animated the character of Geppetto, and became a directing animator. Of all Disney's films, Pinocchio was the feature which Babbitt most admired, and which he regarded as the finest achievement of the studio during the "Golden Age" of animation. Babbitt also animated the characters of the Dancing Mushrooms, Dancing Thistles, Dancing Orchids, Zeus, Vulcan, and Boreas in Fantasia. On the feature film Dumbo, Babbitt was again made a directing animator, and animated the character of the stork. When animating the stork, he made him resemble his voice actor, Sterling Holloway. Babbitt is also credited with developing the character of Goofy, a character which he later described in the 1987 documentary film Animating Art:
Goofy was someone who never really knew how stupid he was. He thought long and carefully before he did anything, and then he did it wrong.
He had previously expounded on Goofy’s nature in a 1930s memo:
Think of the Goof as a composite of an everlasting optimist, a gullible Good Samaritan, a half-wit, a shiftless, good-natured colored boy and a hick. His brain is rather vapory.
During the 1930s Babbitt rose to become one of Disney's best-paid artists, and enjoyed a lavish lifestyle despite the austerity of the Great Depression:
I was living the Life of Riley. I didn't realize how fortunate I was. I was earning a very good salary. I had two servants, a large house, and three cars. You know, what in the world was I going to do with three cars?
However, despite this prosperity, in 1940 he and his wife Marjorie were divorced.