There is a humorous video entitled "Harry Potter: How it should have ended" from the infamous Youtube channel HISHE.
It points out (amongst other things) that, given Snape's nature as a
double agent for Dumbledore in Voldemort's ranks
and his extensive knowledge of potions including anti-venoms:
For your information Potter, Asphodel and Wormwood make a sleeping potion so powerful it is known as the Draught of the Living Death, a Bezoar is a stone taken from the stomach of a goat and it will save you from most poisons. As for Monkshood and Wolfbane, they are the same plant which also goes by the name of Aconite. Well, why aren't you all copying this down?
... should have made him ready for the attack on him by Nagini.
We know an anti-venom does exist, because
Arthur was sent to St Mungo's Hospital for Magical Maladies and Injuries, and was to take a Blood-Replenishing Potion every hour to counter the blood loss that would otherwise cost him his life, but was otherwise fine ... Eventually, Arthur managed to find an antidote to dispel the venom.
Of course Snape could have been caught unaware, but I find this unlikely as he knew how precarious his position was with regards to Voldemort, and his knowledge of Nagini.
Is there any reason he would not have had an anti-venom ready or found some way to immunized himself against the poison?