The soft X-ray spectra of the Virgo and Coma clusters cannot be modeled by emission from the well-known hot intracluster medium attenuated by photoelectric absorption along the line of sight in our galaxy. If the excess soft emission is due to thermal emission in the clusters from gas at about 1 million Kelvin, then the gas should be rapidly cooling. The high rate of cooling poses problems for the origin of the gas and its sink. A model in which the component is due to turbulent mixing layers around clouds scattered throughout the intracluster medium may explain the excess emission. The gas in the mixing layer is reheated after cooling, so that the total mass remains relatively small.