In salaried jobs in the U.S., workers get a certain number of vacation days that they can request to take off work.
When employees and managers are talking about someone's vacation days, they often just call them "days". For example:
Do you have many days left?
I'd like to go ahead and put some of my days on the calendar for next year.
As long as the topic of conversation is vacation, listeners will understand what you mean by "days".