  We analyze AdS and dS swampland conjectures in a three-dimensional higher
spin theory with self-interacting matter, which contains conformal gravity and
is almost topological. A theory of a similar type was proposed as the effective
theory in the high energy phase of non-critical M-theory in 3D. With some
details differing from the usual string theory story, it is found that the
resulting effective theory, namely topologically massive gravity, fits well
into the web of the proposed swampland conjectures. Supporting a recent
proposal, in particular we find that this 3D theory gives rise to a quantum
break time that scales like $t_Q\sim H^{-1}$.
