The speaker of "I Hear America Singing" is the same speaker of all of Whitman's poems: a guy who sounds suspiciously like Whitman himself. Now, it's never a good idea in poetry to confuse the poet with the speaker. Lots of poets like to present their speakers as invented characters. In this case, though, Walt undeniably has a lot in common with this poem's speaker.
The speaker's most distinctive trait is that he loves himself some Americans. He loves boatmen and hatters, stay-at-home moms and washerwomen. He loves watching them work and he loves celebrating their work. The speaker of the poem is all about the regular Joes and Janes, going about their regular business, working their regular jobs, leading their regular lives.
The speaker of the poem finds joy in everyday work, and especially in the people who do that work and so often go unacknowledged for it. He's the type of guy you'd want to be around, probably because he wound compliment you on your hard work stocking shelves at the local supermarket, and then tell you that he loves your singing voice while he's at it.