They could, but given that it'd just make the project later they probably won't. People will always act like you HAVE TO show up and work overtime or weekends,

They could, but given that it'd just make the project later they probably won't. People will always act like you HAVE TO show up and work overtime or weekends, but in reality it's a choice. There may be some consequences, but most likely it'll just be that a manager pulls you into a room and has a talk. I say stand your ground, have a backbone and live your life on your own terms.