A lot of a manager's job IMO is to shield his devs from this kind of deadline pressure and negativity. In the past I've worked under some managers that explicitly told me take my time and get it right and not worry about the deadline. After shipping one of those I later found out that the product manager was so upset with the delay that he was about to call a huge war-room and start micro-managing the project himself. I had no idea we were a week away from that or that anyone was even upset. When I brought it up with my manager he said, that's cause I didn't want you worrying about that. The scale on this one is too important to rush through. He took a lot of heat and deflected it to the point I was totally oblivious and just focused on coding.

I'm not saying this is necessarily always the right approach. It could have back-fired if my manager had judged it wrongly. But what I'm trying to say, is that manager would have never left me alone in a meeting with the PM exposing me to the scenario you describe. Eventually, as I grew more senior it was useful to be exposed to that, but at that point in my career, I really appreciated being shielded from the politics while I just focused on improving my craft.