As someone who is organizing a library fundraiser, you probably worry about what will happen if your efforts do not do as well as you expected. One thing you can do to maximize the possibility of success, though, is to bring the public in on things from the very beginning. Having an Open Day or some sort of other event with refreshments and maybe a local author or entertainer can be a great way to get supporters into the library and seeing what all the fuss is about. If you can show them just what changes are being planned and in what context, your library fundraising idea can be more successful than you expect.
As people wander in and out of the library on an open day, you need to have plenty of volunteers available to show them around, explain what the library fundraiser aims to do, and go over the changes that would be made if the funds were made available. People are more likely to give to a cause if they understand exactly what their money is going to help with, and if they will be able to come in at a later date and see the results of what they helped to support. If you have a running counter somewhere in the library showing how far you are towards achieving your goal, this can encourage supporters to dig deep and make a difference in how well the library fundraising campaign does.