The self-consistency of a microtearing turbulence is studied by computing the electron response via a diffusive Vlasov equation. While the modes are stable in the linear regime, it is shown analytically and numerically that they can be non-linearly unstable. This occurs for beta pol values of order one, in situations where the non-linear radial scale of the current which sustains the perturbation is greater than the linear scale. The associated electric potential fluctuations, which insure the electric neutrality, tend to stabilize these modes unless the non-linear scale is smaller than the ion Larmor radius. This feature imposes an upper bound on the electron diffusion coefficient.