It may be difficult to impossible for a single mom to stay at home and do nothing as Gary Foreman explains, but it isn't impossible for her to stay at home and bring in an income. Working at home has been gaining in popularity over the last decade with both employees and employers, but faster growing than that is the segment of moms who start their own in home business.
Besides doing child care, which is quite popular, bookkeeping, copywriting, proofreading and typing for college students, running errands for the elderly and more, can bring in enough money to live on. Couple that with the stay at home benefits, like not having to buy gas to drive to work, not having to have a work wardrobe, not having to pay for childcare and so on, and almost any woman (or man) can make staying at home work.
It's not too hard to come up with something to be done without working a regular job once your mind is set on it, but if you're still stumped, here are some ideas:
Write at home for content sites. Some people make very good money this way. Content mills often provide residual income based on page views, so you must know a little about promoting your work. Some sites broker content so that you don't work directly for the consumer, but for the company.
Work in customer care. You will need a computer but they will usually pay for your internet. You log into their site and/or use software they provide to chat live (with a script), answer emails or take phone calls. Some companies set your hours and others will allow you to work when you can.
Sell on eBay or something similar. You can make good money if you're alert and pay attention to what is selling and where to get it.
Design crafts. If you're the least bit crafty, you've probably made at least one thing out of your head. Write it down and find an appropriate market for it online. Craft sites are always needing fresh content.
There are many more, but hopefully, this will give you some ideas. If you want to work from home, try it! You might be very pleasantly surprised.