Some (re)reading of the documentation suggests that
ThermodynamicData["Water", "InternalEnergy", {"Pressure" ->
Quantity[0.6*10^6, "Pascals"], "Quality" -> 0}]
works. I specify 0 for saturated liquid and 1 for saturated vapor.
Does that make sense? My answers check with Reynolds and Perkins (2nd edition SI) on page 108.