The Collaborative International Dictionary of English v.0.48:

Exigency \Ex"i*gen*cy\, n.; pl. Exigencies. [LL. exigentia:
   cf. F. exigence.]
   The state of being exigent; urgent or exacting want; pressing
   necessity or distress; need; a case demanding immediate
   action, supply, or remedy; as, an unforeseen exigency. "The
   present exigency of his affairs." --Ludlow.

   Syn: Demand; urgency; distress; pressure; emergency;
        necessity; crisis.
        [1913 Webster]

WordNet (r) 3.0 (2006):

exigency
    n 1: a pressing or urgent situation; "the health-care exigency"
    2: a sudden unforeseen crisis (usually involving danger) that
       requires immediate action; "he never knew what to do in an
       emergency" [syn: emergency, exigency, pinch]

Moby Thesaurus II by Grady Ward, 1.0:

52 Moby Thesaurus words for "exigency":
   case of need, climacteric, clutch, compulsion, constraint,
   contingency, convergence of events, crisis, critical juncture,
   critical point, crossroads, crucial period, crunch, demandingness,
   dire necessity, drive, emergency, exigence, extremity,
   high pressure, hinge, immediacy, imperative, imperativeness,
   importunacy, importunateness, importunity, impulse, impulsion,
   insistence, matter of necessity, pass, persistence,
   pertinaciousness, pertinacity, pinch, predicament, press,
   pressingness, pressure, push, rash impulse, rub, strait, stress,
   tension, turn, turning, turning point, urge, urgency,
   urgent need