Yes and no. It's not  that the employer can literally tell you that you must have someone watch a sick child--that's not their business. But they can tell you that you have to come in for your scheduled hours or shift and that if you don't, you will be fired. What you do then--have a grandparent or sibling watch the child or make some other arrangment--is up to you, but the employer can require you to be at work; they don't have to accomodate you. Some options to explore are using  any paid leave days you have (sick, personal, or vacation) to take the time; or possibly using leave under the Family and Medical Leave Act, though that's most appropriate for chronic or severe illness, not a one-or-two day bout of the flu; also, not all  employers are covered under it (smaller ones are not). Look up "Family and Medical Leave Act" or "FMLA" for more information.