The federal government doesn't supply building money to public libraries, at least not nearly as much as the communities themselves raise. Nor does it supply a large percentage of the operating expenses (in our case, for instance, less than 0.5%).
Public libraries are, by and large, supported by their communities. That might be a district, a city, a town, a village, a county, or, in the case of Ohio, from the State's general fund.
The amount of federal dollars spent is miniscule when compared to the local monies spent.
I expect this to change, probably about 2010, when the US government goes into a "sputnik-style" tizzy over China and India surpassing the US in technology....