In my community, the YWCA has a quilter's club.
Also, some of the stores that sell fabrics have classes or can tell you where they are.
So, find the place where quilters go and see if they would be interested in such an endeavor. After you have a good idea of what you want to do, make a flyer to attract quilters.
People who can't quilt or don't have the time, can donate money or materials. So don't exclude anyone just because they can't quilt.
Here, we have a residential substance abuse program for pregnant women. They learn how to get and stay off drugs while they have a drug-free baby. There are quilters who make sure that all the women get baby quilts.
The only problem I see in what you are saying, is that hospitals have confidentiality issues and won't be telling you which mothers are single or poverty level.
So you have to be willing to just donate the quilts to a peri-natal unit, or to your local police or fire department. The fire department is actually a good option. The people they deal with often have lost everything in a fire, while even a single mom with money issues usually has a baby-shower and gets stuff.
Congratulations to you for being the sort of person who cares about others.