Passive tissue biasing circuitry in an Implantable Pulse Generator (IPG) is disclosed to facilitate the sensing of neural responses by holding the voltage of the tissue to a common mode voltage (Vcm). The IPG's conductive case electrode, or any other electrode, is passively biased to Vcm using a capacitor, as opposed to actively driving such electrode to a prescribed voltage using a voltage source. Once Vcm is established, voltages accompanying the production of stimulation pulses will be referenced to Vcm, which eases neural response sensing. An amplifier can be used to set a virtual reference voltage and to limit the amount of current that flows to the case during the production of Vcm. Circuitry can be used to monitor the virtual reference voltage to enable sensing neural responses, and to set a compliance voltage for the current generation circuitry.