If you can get a Q-Tip, dip it in alcohol, then lightly touch the white spots (most likely mealybugs), then that touch will take care of them. Try not to get any extra alcohol on the plant because it can burn.
I doubt the mealies will kill it, but they can sure weaken a plant. As Tarev said, move it away from any other plants because the mealiebugs can move on to another plant.
I have plants like this that came from my grandmother years ago, so I know what it's like to save a family plant. good luck!
