spider mites wouldn't do that, unless they got really bad. Sounds like mealy bugs.
DON'T USE CHEMICALS!
Mealy bugs develope resistance to chemicals really easily.
Try an insecticidal soap first, or Neem Oil. Just mix a strong mix with water and spray.
First, get rid of badly infected leaves, and wash the plant in the shower with a scrub brush to get rid of all the bugs you can. Mealy bugs are hard to kill as they don't absorb stuff through their shells. Get all you can off of the plant first, then spray it down with insecticidal soap.
Prevent a litter
Fix your critter