Motivated by a question of Ghys, we study obstructions to extending group actions on the boundary ∂M of a 3-manifold to a C-action on M. Among other results, we show that for a 3-manifold M, the S¹× S¹ action on the boundary does not extend to a C-action of S¹× S¹ via homeomorphisms that are isotopic to the identity as a discrete group on M, except in the trivial case M≅ D²× S¹.