Most (if not all) scenarios will have some form of time pressure. Most of the time, this will come in the form of the Feds breathing down your necks: you have a limited window of time to solve the case before they step in and take over. The case has been deemed high enough value that it must be solved, and if your team hasn't figured it out in some pre-set amount of time [two weeks as a first shot, but variable based on specifics, and difficulty of game], the case will be “taken away”.
You are still able to work on the case even when taken away, but you operate under the same conditions as if you were in “off the force” status (GC=0). Your actions are not technically sanctioned, but your characters still desire to solve the case.
Furthermore, while unrelated to time pressure directly, often the force causing the time pressure will at some point be one or more of the “Night Moves”.