Securing American Families Effectively (SAFE) Act - Prohibits the granting of a visa permitting study in the United States, or the issuance of an immigration visa under the diversity immigrant program, to citizens from a country which is on the State Department's list of governments which have sponsored terrorism or which have been less than fully cooperative in anti-terrorism efforts.

Amends the Immigration and Nationality Act to require the Attorney General and the Director of the Federal Bureau of Investigation (FBI) to provide the Secretary of State and the Commissioner of the Immigration and Naturalization Service access to criminal history record information.

Increases: (1) the scope of persons authorized to disclose and use intercepted communications relating to foreign intelligence information; and (2) the period of electronic surveillance orders for non-U.S. persons under the Foreign Intelligence Surveillance Act of 1978.

Authorizes: (1) the FBI Director to expedite the employment of translators; (2) an indictment at any time without limitation for any Federal terrorism offense; and (3) alternative maximum penalties for terrorism crimes.

Provides that any person who attempts or conspires to commit any Federal terrorism offense shall be subject to the same penalties as prescribed for the terrorism offense, with exceptions.

Makes probable cause the maximum standard for authorizing an investigation, or issuing a search warrant related to an investigation, of suspected terrorists.