Senators Feinstein, Leahy and Gregg introduced new legislation, The Social Security Number Misuse Prevention Act, S. 228, to remove social security numbers from public records that are available on the web. Feinstein’s press release is here, and Leahy’s is here.
For background on this legislation, which was introduced in 2001 (as S. 848), with the same title, see this report, Social Security Number Misuse, Identity Theft and The Internet, from the Office of the Inspector General at the Social Security Administration.