The conductance change of nanowire field-effect transistors is considered a highly sensitive probe for surface charge. However, Debye screening of relevant physiological liquid environments challenge device performance due to competing screening from the ionic liquid and nanowire charge carriers. The authors discuss this effect within Thomas-Fermi and Debye-Hückel theory and derive analytical results for cylindrical wires which can be used to estimate the sensitivity of nanowire surface-charge sensors. They study the interplay between the nanowire radius, the Thomas-Fermi and Debye screening lengths, and the length of the functionalization molecules. The analytical results are compared to finite-element calculations on a realistic geometry.