Can a employer make you work hours that you are not getting paid for?

Two different issues here:

First, assuming you are an hourly, not a salaried employee, you have to be paid for all hours worked--period. You may not be made to work without being paid for the hours. If you are salaried and exempt from overtime, you may be made to work any number of hours without additional compensation. If you are salaried but not exempt from overtime, you may be made to work extra hours but need additional compensation for hours worked past 40 in one week. (No extra compesation for working longer than you normally do, as long as you are working 40 hours or less.) There are some salaried staff who are not exempt from overtime--being paid a salary does not, in and of itself, make you exempt from overtime; instead, you need to meet the tests for being exempt, which generally means being an administrative employee without a lot of discretion and authority, being a manager or executive, or being a professional. Go to the Department of Labor (DOL) website to see the tests for overtime exemption.

Second, regardless  of whether and how much you must be paid for the extra work, if you have not completed your work by shift end and the manager feels you should have, he or she could write you up for it, so long as there is no contract or  employment agreement which limits his or her ability to do so. You could be disciplined, suspeneded, demoted, or fired--again, unless you have a contract to the contrary--if your employer wishes it.