I want to agree with that, but I'm not sure we have that sort of culture anymore. Another two seasons without a trophy and the knives will start sharpening. We've seen this already with Rafa. One season and he was out.
Rafa was of a strong character, it's not about ignoring, the media can pick up on a narrative and run with it and it becomes it's own tidal wave. As for Gerrard, I don't want to rehash old discussions, the likes of Gerrard are legends and Carra an important part of our recent history, but they both picked a side when the media narrative was to push Rafa out. At best you can say their loyalties were stronger towards their own opinion of what best served the club rather than their loyalty towards their manager at the time.
Rafa was a more divisive character than Klopp though. Rightly or wrongly (we know it's the latter, but I'm sure it wasn't
all completely unjustifiable and xenophobic... ahem...), he wasn't liked by the majority of his managerial peers and the media, which made it far more difficult for him when results went badly. You combine that with an ownership in Hicks & Gillett which never came close to committing to him for the long-term as FSG have done with Klopp, and the inevitable result is immense pressure and instability every time something goes wrong on or off the pitch.
I honestly think people need to get over their Rafa/H&G insecurities now. It was almost a decade ago. The two situations just aren't comparable in my opinion. Klopp will have tough times and face his own kind of pressure during his time here, of that I have no doubt, it's football after all, but I can't see things ever getting as desperate as that. Nor as desperate as "Give it Gerrard 'til the end of the season" on as wide of a scale as you seem to be concerned about.