More than likely you have spider mites, and unless you're thorough soap water will not kill them. Miticides will work, but spider mites become imune to them quickly. Rubbing alcohol sprayed on half strength will do a better job than soap water.

Grace, if you have spider mites, chances are you are only seeing the pest as a group since it is so small it is detectable only by their numbers...not individually.
The web is a tell-tale sign of them--generally such is seen on the undersides of leaves.

First attach should be by spraying water on them either in the shower or by hand-held sprayer that can hit them to knock them off.
The web will not be so affected so the use of soap and water is one such method. But, reading your post, I sense you are using soap as a more straight approach--the solution may be too heavy soap wise.
Soap is an astringent---leave it on your skin and see what it does. Imagine it drying on the leaves of your plants.
It can easily cause suffocation due to air and moisture not being able to enter the leaf tissue.

Better to use a solution of soap and water in a 2 1/2 percent ratio.....i.e. 1 part soap to 40 parts water.
You can use one teaspoon soap in a bottle normally used to spray...usually having a pint...16 ounces of liquid. That will give you the 2 1/2 percent.
If you feel this solution might be too strong, then just use 1/2 the ratio of soap. That's 80 to 1 ratio.

Spray the plant bottom to top, and then top to bottom and let the solution stay for 10 minutes. Then rinse the plant off with warm water.

If this doesn't control the spider mites, then a dusting program with lime sulfur or petroleum oil can be carried out.

Spider mites can be controlled by regular misting of the plant.

Garden pests such as spider mites usually have a life cycle that is just weeks. So they breed continuously. Their eggs are left in the soil or on the undersides of leaves or in the stem/leaf junctures. The eggs might hatch in a couple days, followed by theilarvae which turn to adults in a few days. the adults then do the whole cycle over again.

By treating the plant every 5 days for 3 application, it is usually reliable to get rid of the pests in that time.
But constant vigil is necessary. Treat the soil as well as the plant.

I treated them with a little insecticidal soap prepared commercially until I ran out this morning. I'll definitely follow you advise for making my own! I'll definitely remember the rubbing alcohol solution as well.

I wonder if it is spider mites. The plants have been inside for a few months. I'll have to watch for webs more closely. The plants that I've seen the webs on are Asparagus Fern....well, that's what I call it.

These are so messy in the winter months but so beautiful in hanging baskets on the deck thru the warm temps. Now that they all have a fresh hair cut, I'll just take them to the bath tub for their treatments and watering in the shower.

Thanks so much for the quick advise! This is the first time that I've been on this forum and was hesitant to post. I'm so glad I did!! LC Grace