Supernovae searches and object-counting surveys have been been suggested as a method for determining precisely the current value and time-variation of the equation-of-state, w, of the dark energy component responsible for the accelerated expansion of the universe. I demonstrate that the methods are fundamentally limited by the fact that luminosity distance depends on w through a multiple integral relation that smears out information about w and its time-variation. The effect degrades the resolution of w that can be obtained from current supernovae data. I conclude that a new (yet to be found) cosmological test is needed to resolve w and its time-dpendence. Some consequences relevant to the cosmological constant problem are sketched.