Overtime should be paid for. Usually the hourly rate + 50%. In that case you decide whether you want to take it.
In the USA, some people have the choice of working unpaid overtime when the company needs it, or quitting. Whoever, since you gave plenty of warning, your company should have changed the way it works, or hired more people. So your company didn't need you to do overtime. Maybe they have no money, that means they have to find that money somehow, it doesn't mean you need to do unpaid overtime.
I'd say start finding a different job, tell them that their plan running with unpaid overtime isn't going to work, and as soon as you find something better, let them suffer.
I don't quite understand the need for "politeness". It's business. If you mean "tell them without swearing" then don't swear. Just tell the facts. It's not impolite to tell someone facts they don't like to hear.
PS. In case someone didn't read past the first sentence: No, in the USA in a salaried position you don't work until the job is done. You work as long as required by the needs of the company. And lack of planning by the company or lack of money to hire more people doesn't create a requirement to work long hours. There are some muskrats out there who believe this, but the are wrong.