Is my cactus sick? Can it be saved
Your cactus appears to have scale insects and the webs that you see may be unrelated. Many spiders create webs on cacti. From what I can make out in your photos, the white scales are slightly bumped up with a dark dot on the top which suggests scale insect.
There are thousands of types of scale insects but those most likely to attack a cactus are from the Diaspididae family. Scale insects prefer shade so they are most likely to pop up on the part of your cactus that is away from its light source. They multiply quickly. When removed, they leave a little mark where they have been feeding on your plant.
To rid your cactus of scale, you will need to remove them physically with your fingernail or some tweezers. Touching them first with rubbing alcohol on a cotton swab may help to loosen them but you should avoid covering the cactus itself with alcohol.
Once you have gotten rid of them, you can treat your cactus with a systemic insecticide that will be taken up through its roots and will keep new insects from attaching. This application can only be done while the cactus is in active growth so the window is closing for this season and you may have to continue to remove them until you can treat your cactus in the spring.
This fact sheet from the Missouri Botanical Garden has a good photograph of scale insect so that you can compare it to what you see on your cactus for confirmation. It also recommends specific systemic insecticides.
Good luck with your cactus!