Yes, in modern history, many Members of the House have been nominated and accepted cabinet appointments in various White House administrations. Below are a few examples that date back to the Kennedy Administration.
Barack H. Obama
Secretary of the Army- House Representative John McHugh (R-NY) pending confirmation
White House Chief of Staff- Former House Representative Rahm Emanuel (D-IL) resigned 2 January 2009 to accept cabinet appointment
Secretary of Transportation- Former House Representative Ray Lahood (R-IL) did not run for 111th, but accepted cabinet appointment by Obama during 111th Congress
Secretary of Labor- Former House Representative Hilda Solis (D-CA) resigned 24 February 2009 to accept cabinet appointment
George W. Bush
US Trade Rep/ OMB Director- Former House Representative Rob Portman (R-OH) resigned April of 2005 to accept cabinet appointment.
Chairman of the Securities and Exchange Commission- Former House Representative Christopher Cox (R-CA) resigned 2 August 2005 to accept appointment.
Director of the Central Intelligence Agency- Former House Representative Porter Goss (R-FL) resigned 23 September 2004 to accept appointment
Drug Enforcement Agency Administrator- Former House Representative Asa Hutchinson (R-AR) resigned 6 August 2001 to accept appointment
Ambassador to the U.N. Agencies for Food and Agriculture- Former House Representative Tony Hall (D-OH) resigned 9 September 2002 to accept appointment
William “Bill” Clinton
Ambassador to Italy- Former House Representative Thomas M. Foglietta (D-PA) resigned 11 November 1997 to accept appointment
Ambassador to the United Nations- Former House Representative Bill Richardson (D-NM) resigned 13 February 1997 to accept appointment
OMB Director- Former House Representative Leon Panetta (D-CA) resigned 22 January 1993 to accept appointment
Secretary of Defense- Former House Representative Les Aspin (D-WI) resigned 20 January 1993 to accept appointment
Secretary of Agriculture- Former House Representative Mike Espy (D-MS) resigned 22 January 1993 to accept appointment
George H.W. Bush
Secretary of Defense- Former House Representative Richard Cheney (R-WY) resigned 20 March 1989 to accept appointment
Ronald Reagan
OMB Director- Former House Representative David Stockman (R-MI) resigned 27 January 1981 to accept appointment
Jimmy Carter
Secretary of Agriculture- Former House Representative Robert Bergland (D-MN) resigned 22 January 1977 to accept appointment
Secretary of Transportation- Former House Representative Brock Adams (D-WA) resigned 22 January 1977 to accept appointment
Ambassador to the United Nations- Former Representative Andrew Young (D-GA) resigned 29 January 1977 to accept appointment
Gerald Ford
None to be found
Richard M. Nixon
Secretary of the Interior- Former House Representative Roger Morton (R-MD) resigned 29 January 1971 to accept appointment
Secretary of Defense- Former House Representative Melvin Laird (R-WI) resigned 21 January 1969 to accept appointment
Vice President of the United States- Former House Representative Gerald Ford (R-MI) resigned 6 December 1973 to accept appointment
Office of Economic Opportunity Director- Former House Representative Donald Rumsfeld (R-IL) resigned 25 May 1969 to accept appointment
Lyndon B. Johnson
None to be found
John F. Kennedy
Secretary of the Interior- Former House Representative Stewart Udall (D-AZ) resigned 18 January 1961 to accept appointment
