"this'll be the day that I die" is a rewording of the line "Cause that'll be the day when I die" from the chorus of Holly's hit 'That'll be the Day', in which the singer fears the worst should his love leave him: for the narrator, his love has left him, and this is McLean's way of both mouring the death of that music and way of life, and pointing to Holly as his symbol of it.
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Tree Frog