The only person I've seen calling for Cathro to go is that weapons grade arsehole Ewan Cameron. I've been pleasantly surprised that the majority of reactions I've seen is that we need to give him time and a full Summer transfer window to work with.
I've just said this on the match thread, but it links up nicely to follow on from your comments on "ripping it up" - Cathro clearly didn't like the squad he inherited. The problem is that the January transfer window is a not good for completely rebuilding a squad, which we've done. So as far as signings go, the only two I think we can clearly start judging in the medium and long term is Isma, as we paid money for him; and Martin, who we gave a three and a half year deal (shudder).
This Summer will another offseason of lots of incomings and departures. That is clear, and needed. The fact we've had such a high turnover of players is an issue I put solely to Levein. He is the one we should be questioning, I think, rather than Cathro at this time.