Meeting the deadline is an impossibility; there is no way we can be ready in time.
(uncountable) The quality of being impossible.
1548, Edward Hall, The Union of the Two Noble and Illustre Families of Lancastre and Yorke, London: Richard Grafton, Henry VIII, year 15,
After long reasonyng, there wer certain appoynted, to declare the impossibilite of this demaunde to the Cardinal,
(obsolete) The state of being unable to do something.