I always assume, perhaps naively, that people are just blowing off steam and are not to be taken literally. Hell, I yell all kinds of crap at my TV during a game, I just try to be more level headed once I head out into public (or online.)
That being said, the "let's give them time" line every 3 years gets a bit old after awhile. Particularly when you see other teams go from worst to first in a single season. Rationally thinking, yeah, you're right, in general it's going to take a little time and it's not this staff's fault. But people are just fed up with giving this team time. I understand it, it's frustrating as hell.