"Maudlin" sketches a portrait of a drunk in just a few lines, and it never quite settles into a single story. The opening image is odd and a little gross: talk that has grown fur, as if words left too long have started to mold. That "discourse" is tied to "the first love of a drunk," which suggests that the drinker's rambling is really a kind of devotion, or that the first love is the bottle itself. The poem doesn't say which, and that ambiguity is part of its pull.
Then the figure becomes more reckless and more sad. He would kiss anybody "for a curse," so affection and insult are almost interchangeable to him. In the last lines he sinks to the ground and stays "in doubt," unsure of where he stands, or of what he wants, or whether anyone cares.
The speaker seems more observer than participant, and the tone is pity mixed with unease. The mood is woozy, tender and slightly shameful, much like the word maudlin itself.