Couple of points, Quizmonster.
Hodie, meaning today, is an adverb of time and cannot be used as the direct object of a verb, which the phrase suggests it is.
Dies can be either masculine or feminine, depending on its meaning. When it refers to a particular or appointed day, as I understand it in this context, it is feminine, hence 'hanc' rather than 'hunc'.
p.s. I don't think that there would be much point in approaching a Roman Catholic priest in this day and age; they were never very good at Latin, apart from reciting it, and most now have none at all.