Listening to HP audiobook on the bus to Portland and made a discovery. At the beginning of "The Lightening-Struck Tower" when Harry tries to get Dumbledore back to the castle and to the hospital wing, Dumbledore repeatedly asks for Snape rather than Madame Pomfrey. I always assumed he wanted Snape to heal him, like he had when Dumbledore put on Marvolo Gaunt's ring.
But perhaps he actually wanted Snape to come and fulfill his Unbreakable Vow. Harry was afraid drinking Voldemort's potion was killing Dumbledore. Maybe he wasn't wrong.