The lowest electronically adiabatic potential energy surface of the uracil anion has been theoretically investigated with density-functional theory methods in order to understand the mechanism of the N-H bond dissociation induced by low-energy electron attachment. We found that the BH&HLYP level can reasonably describe both the dipole-bound and valence anionic states in a balanced way. With this density-functional theory level, we have constructed two-dimensional potential energy surfaces as a function of appropriate internal coordinates and discuss the importance of electronic coupling between the dipole-bound and valence anion states in dissociative electron attachment of uracil. The transition state geometry for the electronic isomerization between the dipole-bound anion and the pi* valence anion was successfully optimized and the barrier height for this isomerization was found to be relatively low. It was found that the out-of-plane motion of H at the C-6 position plays the most important role in this isomerization process. Reduced-dimensionality quantum wave packet calculations taking two active internal coordinates into account have also been performed to interpret the resonance structures observed in cross sections for the N-H dissociation channel at a qualitative level.