Sacrificing to Phyrexian Negator/Obliterator

[TheWhiteDragon]

I have a phyrexian Negator.  I block a 5/6 tarmogoyf.  After damage is dealt, can I sac negator as one of the 5 permanents, or does it die and I have to sac 5 other things?  Same for Obliterator, except the reverse example.  If my opponent blocks with a 5 or less power critter, can it sac the critter it blocks with or is it already dead and off the battlefield from lethal damage before things can be chosen to sacrifice?

Oracle Text: Trample
Whenever Phyrexian Negator is dealt damage, sacrifice that many permanents.

[Chubby Rain]

It's a triggered ability. Damage is dealt, state-based effects are checked (creature dies), and then the ability is put on the stack.