The effective theory which characterizes the low-energy sensitivity of the minimal Weinberg-Salam model to a heavy Higgs boson sector is shown to be the gauged SU(2) L × U(1) non-linear θ model. This theory is the limit of the Weinberg-Salam model as the Higgs boson mass, MH, is removed ( MH → ∞). Using the symmetry properties of the non-linear theory, along with a power-counting analysis, we are able to classify low-energy observables according to their sensitivity to the regulator ( MH). At one loop, the greatest sensitivity is a logarithmic dependence on the Higgs boson mass. The MH dependent corrections to some specific, experimentally accessible observables are calculated, and other possible applications of this technique are discussed.