Recently, TersoffCG, a coarse grain potential for graphene based on Tersoff potential, has been developed. In this work, we explore this potential, applying it to the case study of a single wall carbon nanotube. We performed a series of molecular dynamics simulations of longitudinal tension and compression on armchair carbon nanotubes, comparing two full atomistic models, described by means Tersoff and AIREBO potentials, and the coarse grained model described by means of TersoffCG. We followed each stage and mode of deformation, finding a good matching between the stress strain curves under tension independently from the used potential, with a small difference in the pre-fracture zone. Conversely, under compression the coarse grain model presents a buckling stress almost the double of the full atomistic models, and a more than double post-buckling stress. With the increase of the nanotube diameter, the capturing of the buckling modes is enhanced, however the stress overestimation remains. A decreasing of the three body angular term in the potential can be a rough way to recover the buckling stress, with small losses in the capturing of the post-buckling behavior. In spite of a good agreement under compression, the fracture behavior of the nanotube is strongly influenced, suggesting this modification only when no fractures are present. The findings reported in this work underlie the necessity of accurately evaluate the use of a coarse grain model when compressive loads are applied to the system during the simulation.