Beyond the databases listed below, HathiTrust, a digital repository for major research libraries, is an excellent place to check for scanned, full-text government documents.
Proquest Congressional provides full-text access to Congressional documents from 1789 to present, hearings from 1824 to the present, Executive Branch documents, bills and laws, etc.
HeinOnline provides access to numerous public documents, including titles such as the Congressional Globe, which contains the debates of Congress from 1833 to 1873.
American State Papers are the legislative and executive documents of the first 14 Congresses.
U.S. Congressional Serial Set provides full-text access to the reports, documents, and journals of the U.S. Senate and House of Representatives. Date coverage is 1817 to 1994. The Serial Set does not typically include hearings (though some hearings from the late 19th and early 20th centuries are included).