This is actually a great question, and I usually hate questions of ethics as they are so ridiculous. But yes, I do think it is the ethical duty of an American to temporarily excuse themselves from work to assist with disaster relief projects. I can't think of many things more nobel than this.
What a very child like question to ask of people. Of course it's not their ethical duty. The country can't come to a standstill every time there's a disaster relief project going on, which is what would happen. No. We have disaster management crews, people who are trained to help.
While I'm sure that many Americans would do so if they could, their jobs would not let them. I know that this has nothing to do with ethics, but a man who is trying to feed his family should prioritize their well-being over volunteering for a disaster relief project. For the single man, I think it wouldn't be a bad idea. The only problem is how long would they be able to? Would their next pay check be able to pay for their rent and food? It depends on how their company handles the situation.
If a person chooses to excuse themselves from work to assist with disaster relief it is that person's choice. It is not an obligation or something one should be forced to do. Only the individual can decide if helping is an ethical duty. Some workers may not have the time or means to assist with disaster relief projects.
In today's world, it is not always possible for people to take off work anytime they want to help out with disasters. There are projects to finish, bills to pay, and work to be done. There is no compelling ethical duty to serve in disaster relief if it would result in adverse consequences due to missing time at work.