So you need to invoke conservation of momentum here. The total momentum of the entire system - Mr. Pankey and all his projectiles, is zero. The total momentum imparted to all the spit balls is equal and opposite to the total momentum imparted to him and his chair.
We need to know the total amount of spit he spat:
O.K., so it's a lot...
Need to convert this into number of spit "projectiles"...
...So he would have to spit 10,000 times. (10 kg / 1 g)