Have you ever noticed that when there is a high profile case in the news, that people offer to adopt that poor, abused dog in droves, and people donate - in droves? The truth is, when you reach out to the public, genuinely reach out, people will help you. They love to help animals in need. People stay away from municipal animal pounds because they are depressing, because the workers there look at everyone as animal abusing scum, because they are rude, cold, and unhelpful (at least, this is the experience you receive at the shelters in my area). Take away all that, staff the shelter with friendly, helpful, nonjudgemental faces, aggressively market your animals with nice photographs and upbeat, descriptive bios, participate in adoption events in your area, and make your shelter a place where people want to come to adopt and a place that people want to support, and you will have the resources you require.
The no-kill shelter I volunteer for gets donations out the wazoo. There are single donations of $5000 at times to this place. I once helped type up spreadsheets of donations so that thank you notes could be mailed out, and in one month, they had $30,000 in donations! That was December which may make a difference since it is the Christmas season and all, but I know that they get a lot of money from people all the time, and it really isn't that hard.
And honestly, you can't truly improve the care and overall efforts in the shelter until you stop the killing. While the killing of healthy adoptable pets is allowed to continue, the people who work there will distance themselves from the animals because its easier to NOT CARE about something that is going to die anyway. It is easier to slack on disease prevention, why provide more than the bare minimum (if that) when the animal is probably just going to die anyway?