It depends on what this person is referring to. If it is something illegal or dangerous, then yes, they cannot force you to do it. That would be illegal.
If it is unpaid overtime and you are an hourly employee, then no, if that is not part of your contract.
If you are on salary, then you may need to remind them there needs to be compensation with time off if they are not going to pay. This may even mean in set or promised future..
I know in Retail as a buyer, I was on salary and during the holidays it was expected we be there as needed if not enough sales people appeared and we were to make sure we worked the extra hours that the store would be open.. But later in Jan and Feb , we would be able to take off some time to make up for it.
We also knew that just because I was buyer, did not mean if none of the custodians showed up I would not be expected to mop the ladies room or help throw out the trash.. We did what ever it took to keep the store running.
If it is just your job, then this is the bottom line. You can do the work and what ever needs to be done or you can make the choice that you do not want to stay there.