Although Josh Lyman makes a lot of insulting Wisconsin jokes, Bradley Whitford is actually from Wisconsin.
The piano piece played at the end of the episode is Frédéric Chopin's "Revolutionary" Etude, Op. 10 No. 12 in C Minor.
The title refers to a Korean cultural concept, as described by Jed Bartlet: "There is no literal English translation. It's a state of mind. Of soul, really. A sadness. A sadness so deep, no tears will come. And yet still there's hope."
The piece played by Jai (Tony Lee) to illustrate the feeling of "han" is Frédéric Chopin's Prelude Op. 28 No. 4. After looking up the meaning of the word, the President (Martin Sheen) explains it as "a sadness so deep no tears will come, and yet still there's hope."