There are actually many libraries in the US and worldwide that have embraced individual concepts outlined in the Tablet Library Manifesto, but there remains many issues outside the hands of public libraries that control what can be done to move all of the concepts forward, most important of which it copyright law.
As for existing public libraries that come close to the Tablet Library model there is a library in Bexar County, Texas that claims it has the first all digital Public Library in the united states. The Bexar County BiblioTech library will offer 10,000 e-books to the county’s 1.7 million residents as well as the opportunity to read them on 600 e-readers and 48 computer stations in the library.
In 2009 the Fisher-Watkins Library (academic library) at Cushing Academy of Ashburnham, MA, got rid of its 40,000 books and replaced them with electronic sources. During the overhaul all resources were converted to digital formats, and the library's Web site was redesigned to provide students and faculty with online resources and tools on a 24/7 basis. Read more about it here.