Reading a book or poem so carefully (while constantly referencing the OED), that you suddenly discover something "new and special" about one word in the poem. This word then magically allows you to write three paragraphs about its "new and special meaning." All the while during this "close reading," you will be contemplating suicide as your face, body, and mental thought process will hurt with the agony of forced close analysis.
Bob: I've got a twenty seven page paper due tomorrow on a four line poem.
Chris: Man you better do a close reading of that poem.
Reading a book in a state of exhaustion, resulting in ones face dropping steadily closer to the page.
I was at the library doing some close reading. Woke up and I had dissolved several verses of Keats in drool.