I believe that it is true that members of a public library board, sometimes called trustees, can be the very best tool that library has. I also believe it is imperative to educate them so that they can be as effective as possible. In matters of advocating for the library, and its budget, I was once told that “testimony from a trustee is better than from a librarian, and testimony from a Friend is better than a trustee.” The point being that the municipal boards that approve your budgets tend to think that a librarian wants more money for the library to make the librarian’s life better/easier; but a trustee is a taxpayer elected to look out for the municipality, its citizens, and make wise choices about spending tax money (and in fact, helping to determine how much to levy on the taxpayers.)
The post “Trust in Your Trustees” by Will Manley makes the same point (and others), more eloquently than I can. In the example he gives, the board asks for money for 3 new positions, and is awarded enough for FIVE. This is obviously (and sadly!) not something that is likely to happen in the current economic environment—but the point is still a valid one.
So educate your trustees. And then trust in them. Good luck.