An away win at Anfield gives a lot of goodwill mate. As do cup runs.Exactly.
I don't see it as a glass ceiling, it's all fixable.
Whether Martinez can/will fix it, tough to say. He's fixed some things during his tenure but also failed to deal with potential issues that exacerbated over time. Needs to pick up results in the short term to get people back onside, and that should be his first point of call.