The original law required a court order for any surveillance conducted on U.S. soil, to protect Americans' privacy. The White House argued that the law was obstructing intelligence gathering.
The most contentious issue in the new legislation is whether to shield telecommunications companies from civil lawsuits for allegedly giving the government access to people's private e-mails and phone calls without a court order between 2001 and 2007.
Some lawmakers, including members of the Senate Judiciary Committee, appear reluctant to grant immunity. Suits might be the only way to determine how far the government has burrowed into people's privacy without court permission.
The committee is expected to decide this week whether its version of the bill will protect telecommunications companies.
The central witness in a California lawsuit against AT&T says the government is vacuuming up billions of e-mails and phone calls as they pass through an AT&T switching station in San Francisco.
Mark Klein, a retired AT&T technician, helped connect a device in 2003 that he says diverted and copied onto a government supercomputer every call, e-mail, and Internet site access on AT&T lines.