The Collaborative International Dictionary of English v.0.48:

Urgency \Ur"gen*cy\, n. [Cf. F. urgence.]
   The quality or condition of being urgent; insistence;
   pressure; as, the urgency of a demand or an occasion.
   [1913 Webster]

WordNet (r) 3.0 (2006):

urgency
    n 1: the state of being urgent; an earnest and insistent
         necessity
    2: pressing importance requiring speedy action; "the urgency of
       his need"
    3: an urgent situation calling for prompt action; "I'll be
       there, barring any urgencies"; "they departed hurriedly
       because of some great urgency in their affairs"
    4: insistent solicitation and entreaty; "his importunity left me
       no alternative but to agree" [syn: importunity, urgency,
       urging]

Moby Thesaurus II by Grady Ward, 1.0:

75 Moby Thesaurus words for "urgency":
   antecedence, antecedency, anteposition, anteriority, blandishment,
   buttonholing, cajolement, cajolery, case of need, clutch, coaxing,
   compulsion, constraint, crisis, crunch, demandingness,
   dire necessity, dominion, drive, dunning, emergency, exigence,
   exigency, extremity, front position, high pressure, immediacy,
   imperative, imperativeness, importance, importunacy,
   importunateness, importunity, impulse, impulsion, insistence,
   matter of necessity, nagging, necessity, need, persistence,
   pertinaciousness, pertinacity, pestering, pinch, plaguing, plying,
   precedence, precedency, preceding, precession, precursor,
   predicament, preference, prefixation, prelude, press, pressing,
   pressingness, pressure, priority, prothesis, push, rash impulse,
   seriousness, stress, superiority, teasing, tension, the lead,
   top priority, urge, urgent need, urging, wheedling