We show that daily sunspot area can be used in a simple model to reconstruct daily variations in TSI. The model assumes that all TSI fluctuations can be traced back to the emergence of sunspots on the solar disk. Cotemporal data for TSI and sunspot area are analyzed to extract the detailed impulse response function that describes the time evolution of TSI in response to a sunspot that is a delta function. The impulse response function clearly shows the evolution of a dark sunspot into a well-defined bright region which then spreads out and decays over a period of about 500 days. This function can be used to produce a daily TSI record from the Greenwich daily sunspot area database, which extends from the late 1800's to the present. The reconstructed TSI shows little long-term trend in the level of TSI at solar minimum.