Let’s roll back to the time when the poem was written. That was a time, that we consider to be the birth of America, as a nation with the democratical political system. Thus, there is no wonder this strong issue was included into a poem of Whitman. We all know, that poetry comes out from the strong emotions, like grief, love, or, in this case, from inspiration.
When reading, it becomes apparent, that Whitman overthinks his personal experience and includes it in the extended political scene. Also, we should remember, that the ‘self’ Whitman expresses in his poem is an embodiment of the self-reliant man of Emerson. This ‘self-reliant man,’ as you might remember, is a man, who seizes the diverse nature of America and all the people living in it.
Loads of researchers state that this poem is some kind of author’s solution to the crisis of the union, which was about to grow into the civil war. Also, the poem is considered to be the presentation of the America’s ‘self’ in its fullest sense. Critics state this poem to be one of the most representative among Americal Literature works.
If you look for a quotation, where the reference to the democracy is seen clearly, I suggest you to this one:
I speak the pass-word primeval, I give the sign of democracy,
By God! I will accept nothing which all cannot have their
counterpart of on the same terms.
Hope it helps!