We consider the mechanism for very slow relaxation in a supercooled liquid in the framework of the self-consistent mode coupling model. The short time dynamics in the model is taken into account through the inclusion of the bare transport coefficient while the cooperative dynamics over different time and length scales is approximated through the mode coupling terms. A lower cutoff time t(0) for the memory functions representing the long time dynamics is considered in order to account for the contribution coming from the bare transport coefficients. In the present work, we have investigated the implications of this cutoff time (t(0)) for the asymptotic dynamics in the supercooled regime, Our calculation shows that the self-consistent approach results in slow relaxation times typical of what is seen in the fragile liquids at temperature high compared to the glass transition temperature with a power law increase around a critical temperature. It however does not give rise to the very sharp increase in relaxation time scales for any reasonable approximation for t(0) in a fully self-consistent calculation.