The capsids of certain Archaea-infecting viruses undergo large shape changes, while maintaining their integrity against rupture by osmotic pressure. We propose that these capsids are in a smectic liquid crystalline state, with the capsid proteins assembling along spirals. We show that smectic capsids are intrinsically stabilized against the formation of localized bulges with non-zero Gauss curvature while still allowing for large-scale cooperative shape transformation that involves global changes in the Gauss curvature.