In 3D, arbitrarily weak disorder in superconductors with line nodes gives rise to a nonzero Fermi level density of states {ital N}(0), leading to characteristic low-temperature thermodynamics similar to that observed in cuprate and heavy-fermion systems. In a strictly 2D model, possibly appropriate for the cuprates, it has been argued that {ital N}(0) vanishes. We perform an exact calculation for a 2D {ital d}-wave superconductor with Lorentzian disorder and find a nonzero {ital N}(0). For other continuous distributions we obtain a nonzero lower bound for {ital N}(0). We discuss the reasons for this discrepancy. {copyright} {ital 1996 The American Physical Society.}