You have a significant other, and also have a strong friendship with someone else. The relationship has strict boundaries to remain as a friendship. However, instances occur, which could be perceived as more than "just friends" behavior.
Jane was dating Dave. Dave neglected Jane. Jane met John. John and Jane became "friends" and proceeded to blur the line, when drunk, between being friends and more.
A reference to snorting cocaine
. When a user uses a rolled dollar bill, he/she has to lean in close to snort a line of coke. Human eyesight generally starts to blur at a distance from the eyes of 6 inches. Using a bill requiers a user to get within 4 inches of the coke line, thus, the line is blured.
Tonight my friends, we blur the line.