In most services, the treating physician is rotating on a weekly basis. That's pretty much the most convenient/tolerable/safe period of continuous work, as long as you do not receive more than 2-3 calls per night.
Call number is dependent on the acuity of patients' condition, and the ability of the house staff (i.e. residents on site) to manage minors problems without immediately consulting the attending by phone.
I speculate whether we could have duos who rotate with each other, rapidly trading naps and duty & working closely together, over say a 48, 72, or 96 hour period. Barring emergencies, each gets 12 hours rest a day, and from the patient perspective they function as a tag team. But, not a healthcare professional.