How specifically did comic books reflect or contribute to New Deal America in the 30s?

Hello! You have a very interesting question. Comic books both reflected and contributed to the popular culture of New Deal America.
Some of the most well-known characters of the comic book industry were created in the 30s, just as America was starting to crawl its way out of the Great Depression. Entertainment was very much a form of escapism, but the heroes had changed. American audiences no longer trusted the idea of the "self-made man" who became rich, because they had seen what greed had done to the economy. They also did not swing the other way and pick leftist heroes from reality. Instead, they found heroes in comic-book-form who could be both an "everyman" reflection of themselves and the thrilling hero who can do things normal people cannot do.
Superman's popularity helped take those values that the writers felt were uniquely American—confidence, sense of justice, care of the poor, valuing people over money—and fed them to the wide audience of readers he had. One also needs to look at the creators of these characters, and many writers of comic books at the time were Jewish. For them, these characters—very much in particular Superman—was a reflection of what they thought it was to be truly American in a country that still struggled with accepting Jews as Americans. Superman's comics also dealt with him dispensing justice to everyone—something that a lot of Americans of the time wanted to see from Washington. Many of Superman's early adventures had him doing everything from stopping abusive husbands to hunting down company owners who valued money over their workers. Even though he was not born in America, there was the idea that he was raised with American values, and that became a central theme for Superman comics during the New Deal era. The comics were both explicit and subtle about echoing FDR as he fought for New Deal policies and helped form a popular culture that reflected the celebration of the common man and the rejection of corporate greed.
Sources: 
Comic Book Nation: The Transformation of Youth Culture in America - Bradford W. Wright
Captain America and the Struggle of the Superhero - edited by Robert G. Weiner
"Was Superman a New Dealer?" - Essay by Robert Parkinson (link below).