Half-Blood Prince doesn't say exactly when a death from a broken Unbreakable Vow will occur:
"An Unbreakable Vow?" said Ron looking stunned. "Nah, he can't have . . . . Are you sure?"
"Yes, I'm sure," said Harry. "Why, what does it mean?"
"Well, you can't break an Unbreakable Vow . . . ."
"I'd worked that much out for myself, funnily enough. What happens if you break it, then?"
"You die," said Ron simply.
Harry Potter and the Half-Blood Prince - Chapter 16, A Very Frosty Christmas - Pages 325-326 - Scholastic Books
So, there's nothing written in stone (i.e. canon!) about when death from a broken Unbreakable Vow will occur. However, we can look at other spells and hexes that are capable of causing death. Avada Kedavra causes immediate death. Sectumsempra acts immediately upon being cast. The Fidelius Charm also acts immediately (and while Fidelius doesn't in itself cause death, its Secret Keepers are in constant danger of death once the charm is cast). Moody demonstrated in Goblet of Fire that both Imperius and the Cruciatus Curse act immediately upon being cast.
Yet, we also see slow-acting magic in canon. The most obvious example is Dumbledore's hand, which was fatefully injured by the magic protecting Tom Riddle's ring when Dumbledore tried to put it on. Snape spent almost a full year keeping Dumbledore alive; however, the curse would have eventually killed him. This is one example.
I believe, based on consideration of a variety of spells, charms, and hexes, that death from breaking an Unbreakable Vow would be instantaneous.