How can we apply Homi Bhabha's theory on stereotypes and the notion of the stereotype as a fetish on a poem like Walt Whitman's "The Sleepers," or...

Homi Bhabha's understanding of the stereotype is that "ambivalence" is central to its discursive power. That is, "if the essential duplicity of the Asiatic or the bestial sexual license of the African...needs no proof," if it were already empirically understood, we would not need to keep saying that these notions are so. Moreover, according to Bhabha, the stereotypes "must always be in excess of what can be empirically proved or logically construed." 

The purpose of the stereotype is to offer "a secure point of identification." However, in another place and at another time, the stereotype may be "misread."

Fetishism is a method of making that which you are not a site of "delight and fear." 

Knowing this, let's examine Passage 6 in "Sleepers." A "red squaw" comes to breakfast. Interestingly, it is not the male narrator who is fascinated by her, but instead, it is his mother:

"My mother look'd in delight and amazement at the stranger, She look'd at the freshness of her tall-borne face and full and pliant limbs, The more she look'd upon her she loved her, Never before had she seen such wonderful beauty and purity..."

Because we learning about the mother's fascination through the male narrator's remembrance, we are getting a voyeuristic account which may have less to do with the mother's interest and probably more to do with that of the male narrator's who is focused on the squaw's "wonderful beauty and purity."

This passage in "The Sleepers" is interesting from a contemporary theoretical perspective, not only because it reflects Bhabha's notions of fetishism, but also because it is an instance in which the male gaze (see: Laura Mulvey) is imposed on a woman regarding another woman. 

If you wish to explore the possible stereotyping of Native Americans in another Whitman poem, I would consider, "Song of the Redwood Tree." In that poem, Whitman refers to the new settlers as "a loftier strain" and "a swarming and busy race settling and organizing everywhere...Clearing the ground for broad humanity, the true America..."

To whom is he referring? Whom would this group of settlers be juxtaposed against? Also, consider Whitman's use of anaphora and his continual use of certain synonyms in this poem. What impact does this language have? What purpose does it serve in his overall message?

It is important to know that Whitman strongly favored American republicanism, believing that the nation's democratic principles were most righteous. For this reason, he was a proponent of Manifest Destiny. One could argue that Whitman's "stereotyping" of Native Americans (and, in some poems, of black people) was necessary to construct the republic he envisioned.