Nowadays, 1.5 billion people suffer from chronic pain. Current neuropharmacology and neurostimulation treatments are associated with suboptimal efficacy, due to a lack of understanding of the pain system. A major contributor to many persistent clinical pain states is the phenomenon of central sensitization---a state of hyperexcitability of the pain system resulting from changes in the properties of neurons and circuits within the dorsal horns of the spinal cord. Although spinal cord circuits and their plasticity are challenging to study experimentally, only a handful of computational studies have tried to understand this system with mathematical models. In addition, the high dimensionality of these conductance-based models often limits the possibility to reveal the key mechanisms that modulate the functional state of these nociceptive circuits. As a first step to fill this gap, we built a low-dimensional, integrate-and-fire model of the projection neuron in the dorsal horn. This model aims at capturing the rich dynamical firing activity of the projection neurons: tonic firing, plateau potentials, and endogenous bursting. This study discusses the importance of regenerative and restorative feedbacks at the cellular level in different time scales. We exploited the time scale separation between the dynamics of the ion channels of these projection neurons. Each type of ion channel is associated with a time scale and with either regenerative or restorative feedback. Then, we use an incremental approach to build our model one time scale at a time to understand their effect separately. We showed that the key mechanisms behind the excitability of dorsal horn neurons rely on a specific balance between regenerative and restorative ion channels spread across four time scales. These results suggest that the excitatory and inhibitory interneurons could control the excitability of projection neurons through metabotropic receptors that can modulate the intrinsic membrane properties of the projection neurons.