I am in that situation right now. Management has decided that a product needs to be rolled out ASAP so some people are working late and weekends. I play an important part in the project but I usually get my stuff done during normal working hours. However, there is a lot of subtle pressure to stay around in case the people working need something. If you are a "team player" you stay.

I don't want to let down others (with whom I have a good relationship) but I also don't want to kill my personal life because management has set an artificial deadline so I have a made a conscious decision to limit overtime only to the times when I actually have something to do.

The overtime cult is an insidious force that's hard to resist. Once a few people start doing it there is a lot of peer pressure on others to do it too. I guess it's a dynamic management can exploit to get more work out of workers by playing them against each other.