We show that daily sunspot area can be used in a simple model to reconstruct daily variations in the total solar irradiance, S. The model assumes that all fluctuations in S are correlated with the emergence of sunspots on the solar disk. Cotemporal data for S and sunspot area are analysed to extract the finite impulse response function that describes the time evolution of S in response to a sunspot. 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 400 days. This function can be used to reconstruct S from the Greenwich daily sunspot area database, which extends from the late 1800's to the present. We find that the level of S at solar minimum has no long-term secular trend that is correlated with the level of sunspot activity.