What kind of bug builds webs in the evergreens in Oregon? These webs can be sprayed out with a jet stream of water - but will be rebuilt within a day or two. Where the webs are seems to dry out the plant. Will it kill it? How do I get rid of the pests?
Sounds like spider mites. They are very small and you don't mention "seeing" an insect. I don't use insecticides so would continue to wash them off but you can take a sample branch to a good nursery and ask for identification. Spider mites are common when the air is dry and are very common on houseplants. The web is helpful in determining what they are and a close examination will help you see them. Insectical soap may help and is sprayed on the plants.