Perhaps a good way of looking at the question is to look at one of the most "American" of American authors, Mark Twain. He was considered one of the first to capture a real spirit of the new nation with his use of the vernacular of various regions and the telling of the tales of the places of America that were so different from Europe and other places.
Critics point to his specific knowledge of the places he knew about and the very different ideas and attitudes of the people he wrote about including characters like Huck Finn and Tom Sawyer and those around them both. He also wrote a great deal of journalistic pieces and wrote about the various places he visited which captured in a non-fiction way the spirit of those places.
The term "literary canon" refers to a classification of literature. It is a term used widely to refer to a group of literary works that are considered the most important of a particular time period or place. For example, there can be a literary canon comprised of works from a particular country, or works written within a specific set of years, or even a collection of works that were all written during a certain time period and within a certain region. In this way, a literary canon establishes a collection of similar or related literary works. Typically, works are organized by “period” for example, such as the Early National Period from 1775 to 1828.
The Early National Period of American Literature saw the beginnings of literature that could be truly identified as "American". The writers of this new American literature wrote in the English style, but the settings, themes, and characters were authentically American. In addition, poets of this time wrote poetry that was relatively independent of English precursors. Three of the most recognized writers of this time are Washington Irving, James Fennimore Cooper, and Edgar Allan Poe.
Scholars who specialize in certain periods publish anthologies containing works that they deem important or essential to a particular period. The publisher "Norton" has compiled several anthologies containing what they believe to be the canon for a particular era and periodically updates them. One recent development in literature is the addition of female authors to well-established canons. (There are online lists as well.)