1
general::
Also, at short notice. With little advance warning or time to prepare, as in They told us to be ready to move out on short notice. The noun notice here is used in the sense of "information" or "intelligence." [Late 1700s]
American Heritage Idioms
2
general::
Phrase(s): on short notice
quickly and without a timely notification of other people; with very little lead time. • She called the meeting on such short notice that we had no time to prepare.
McGrawhill's American Idioms And Phrasal Verbs