The "Public Safety First Act" amends the Immigration and Nationality Act to significantly expand the categories of aliens subject to mandatory detention by the Secretary of Homeland Security. It specifically targets aliens who are inadmissible under certain provisions related to unlawful presence, misrepresentation, or document requirements. Under this bill, DHS must detain these inadmissible aliens if they are charged with, arrested for, convicted of, or admit to committing acts that constitute essential elements of offenses such as burglary, theft, larceny, or shoplifting . The mandate also applies to those involved in assault of a law enforcement officer or any crime resulting in death or serious bodily injury to another person. The legislation further requires the Secretary to issue a detainer for such aliens and to expeditiously take custody if they are not already detained by Federal, State, or local officials.