Closing Time

A question for my retail techs out there -

What do you do when it's closing time (either for lunch or for the day) and there's still a LONG line of people waiting? Once it hits closing time and if there's only a person or two I'll get them, but lately it's been so busy that every time we close there's usually 3-6 people still in line. My lovely corporate overlord doesn't allow us to get unapproved OT so I can't stay. I've tried telling the line like 5-10 mins before closing I won't be able to get to everyone and no one leaves. Then they get angry when I close and say I can't take anyone else. Any thoughts or tips on how to deal with this?