there was no such thing as a day off for a priest. But, here in Sun City, AZ a N.O. priest had his day or 2 off. A parishioner of many years died and the spouse asked for the priest. Sorry, says the secretary, he is off golfing. Well, to make a long story short that spouse left the N. O. for the traditional. And in fact, that secretary told that spouse to phone another parish herself!, for another priest.
Well, today, if you are in a hospital and you are catholic asking for a priest, you get whoever is on duty. Yes, a rabbi even and he or she will say a rosary with you or such for all the sects, do all the other sects! They are especially trained.