For a three-cycle arbitrarily polarized laser pulse propagating in the $z$ direction, we calculate the $({q}_{x},{q}_{y})$ momentum distribution for strong-field ionization of atomic hydrogen. We consider the Keldysh theory for a few-cycle pulse and compare the results obtained by evaluating the transition amplitude numerically with the results obtained by evaluating the transition amplitude using the saddle-point method. We show that the validity of the latter depends highly on the ellipticity for fixed peak intensity. This dependence and the range of applicability of the saddle-point method is qualitatively explained by a semiclassical model.