Eh, my personal experience has been that no one actually asks you to stay late for anything. A couple of people seem to do so without being asked, but if a deadline is missed, the reaction is generally, "Well, let's examine the process for what we're doing wrong. Are we overcommitting? Were the specifications wrong? Are the engineers being randomized too much? Did we change the specs midway through?" Etc. It's never "Oh, you didn't put the extra hours in."
In the mid '90s I had a job working in a company doing logistics software. Every Friday about 2:00 my manager would come around and say "We're really behind on our delivery, so the team is coming in tomorrow for a half day. I'll buy everyone pizza for lunch."
On Saturday, of course, things wouldn't go as expected. Many times we were still there at midnight, and he came around asking us to stay for just one more hour so we could help test the latest build. Then there were more problems, so he'd ask us to come in on Sunday. For just a half day.
This happened probably three weekends out of four the first year I was there. It got to the point people were taking Friday off because they figured each hour of vacation was actually worth three hours.
So I came to the realization it was either put my foot down or find another job, so one Friday I went into his office and said "Don't even ask me to come in on a weekend. Ever again." I thought it might cost me my job, but that was the end of it.
But that's just my personal experience.