。
I kept putting it off until the very last minute.
Literal
I [topic-は] last-minute-[mimetic-ぎりぎり] [to-に] become [until-まで] postponement-[as-に] was-doing-[continuous-polite-past-ていました].
ぎりぎり is a mimetic-derived noun/adverb meaning 'at the very limit, barely in time, cutting it close' — often used for deadlines one is about to miss. 先延ばしにする is the set phrase 'to postpone, to put off,' built from 先延ばし ('pushing forward') + にする. The ~ていた past continuous emphasizes the sustained habit of procrastination up to the present moment of the narration. ぎりぎりになるまで means 'until it becomes last minute.'