  We study the consequences of quark matter nucleation in cold hadronic matter
employing three relativistic-mean-field (RMF) models to describe the hadronic
phase and the Nambu-Jona-Lasinio (NJL) model for the quark one. We explore the
effect of a vector interaction in the NJL Lagrangian and of a phenomenological
bag constant on neutron stars metastability. We delineate the region of
parameters of the quark phase that allow for the formation of stable hybrid
stars with mass compatible with the almost $2 \ M_\odot$ pulsars PSR J1614-2230
($1.97 \pm 0.04 M_\odot$) and PSR J0348+0432 ($2.01 \pm 0.04 M_\odot$). It is
shown, however, that not all hybrid star configurations with $\sim 2 \,M_\odot$
are populated after nucleation.
