The child's name has not been released.
Houston Homicide Sgt. Richard Rodriguez says police got lucky because the couple were halfway to California with the child when they were caught early Saturday sleeping in a parked car in Las Cruces, N.M.
Rodriguez told the Houston Chronicle that the mother's friend kept the child overnight Thursday. The woman told the mother to meet her in two different places Friday to pick up the child but the woman never showed up. The mother called Houston police Friday evening.