Can someone explain the ability for Whispering Specter to me?

Say the opponent already has 3 poison counters. My turn is coming up and all his/her creatures are tapped. I attack with my Phyrexian Crusader and my Whispering Specter. The opponent now will get 3 poison counters. Now can I use Whispering Specter's ability? Which is, whenever Whispering Specter deals combat damage to a player, you may sacrifice it. If you do, that player discards a card for each poison counter he or she has. Is that how it works?