  We discuss the resummation of the potentially large O((\beta_0\alpha_s)^n)
QCD corrections to the total cross section of the process e^+e^- \to t \bar t
near the threshold. In this approximation, the cross section factorization into
the short- and long-distance parts is valid. The short-distance correction is
reduced to the production vertex renormalization. It amounts to -9.5% and is
well under control. The long distance corrections are accounted for as the
effect of the coupling's running in the QCD potential. We argue that the
accuracy of present predictions for the cross section in the scheme with the
running QCD coupling is about 10%.
