Can your employer demand a doctors note if you have been out one day?

Yes, they can. Employers can generally "demand" just about anything. Since they are asking for one, it sounds like they require a note to prove a true illness. It may be in your best interest to provide one (in the future, even if you can't this time) as they may treat absences with a note with more leniency than absences without one.

Then again, they may not. Is there an employee manual that lays out an attendance policy?

Was this absence related to intermittent FMLA leave? Or just, I have a terrible cold, I'm not coming in today. :confused: