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Roughly, such a theory assigns a filtered chain complex over Z/2 to a link diagram such that (1) the E_2 page of the resulting spectral sequence is naturally isomorphic to the Khovanov homology of the link; (2) this filtered complex behaves nicely under planar isotopy, disjoint union, and 1-handle addition; and (3) the spectral sequence collapses at the E_2 page for any diagram of the unlink. We prove that a Khovanov-Floer theory naturally yields a functor from the link cobordism category to the category of spectral sequences. 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