How do you motivate people to work overtime to meet a deadline? I have a deadline one week away, and we have set up pretty extensive expectations with the client. Should I talk to the client to try to manage the expectation? If they work overtime, do I have to stay with them, or will that anger them more? This is the first time in our project where I'm pushing for overtime. I do feel like I can do a better job managing expectations next cycle.

Your primary job is to manage expectations. It's your fault to have such high expectations, so negotiate with the client. You may have tight deadlines only if they are connected with external factors (like media promotions, legal regulations, etc.) and not just because the client wants it as soon as possible (the client always wants it as soon as possible).

If you need the team to work overtime, stay with them and provide them with everything they may need - coffee, dinner, etc. Be clear why the overtime is needed, what they will receive as a compensation and what steps you would take to avoid overtime next time.