  We consider a nonlinear $L^2$-critical nonlinear Dirac equation in one space
dimension known as the Thirring model. Global well-posedness in $L^2$ for this
equation was proved by Candy. Here we prove that the equation is ill posed in
$L^p$ for $1 \le p < 2$, and in the massless case also in $H^s$ with $s < 0$.
