A recently developed diabatic representation for the two lowest (2)A(') electronic states of the NaFH system [M.S. Topaler, D.G. Truhlar, X.Y. Chang, P. Piecuch, and J.C. Polanyi, J. Chem. Phys. 108, 5349 (1998)], augmented with highly accurate multireference configuration interaction data, is used to construct a new potential energy function for the ground electronic state of NaFH. The refined potential is used to calculate the bound and quasibound rovibrational states of the Na ... FH molecule. The focus is on the quasibound states corresponding to excitation of the H-F mode in the complex, although states in which the H-F mode is not excited are also studied. All rovibrational calculations are performed within the framework of the Sutcliffe-Tennyson Hamiltonian for triatomic molecules. The energy positions and lifetimes of quasibound states are obtained using the stabilization method. Three methods are employed to solve the rovibrational problem: (i) the variational approach, in which the Hamiltonian matrix, as defined by a discrete basis set, is diagonalized, (ii) the coupled-channel method, in which the van der Waals stretching coordinate is handled by direct numerical propagation on a grid, and (iii) two perturbative approaches based on the adiabatic separation of vibrational motions. The effect of rotational excitation on the lifetimes of calculated resonances is studied. The main results of this study are the strong evidence for the existence of many long-lived rovibrational resonances corresponding to excitation of the H-F mode in the complex and the rationalization of this finding in terms of effective potentials defining adiabatic separations. Possible impact of the results obtained in this study on new experimental ways of probing potential energy surfaces of the NaFH system, with emphasis on the dynamics of photo-induced charge transfer in Na ... FH, is discussed.