last minute

Short definition from Wiktionary

Noun

1. 1
   An arbitrary (non-specific) point in time, too close to a deadline to reasonably begin a critical task.

Adjective

1. 1
   Very close to a deadline.
2. 2
   Just before it is too late; in the nick of time.
3. 3
   Done or occurring at the latest possible time before an event.