Karl Meyer and Shareen Blair Brysac suggests exactly that in the Washington Post:
Amid the blizzard of résumés blanketing Washington as the Obama era dawns, there is a superbly qualified candidate for full employment whose name has been overlooked. We refer, of course, to William Jefferson Clinton, America’s 42nd chief executive and commander in chief. Yet now, by a wonderful combination of circumstances, comes an opportunity to harness his unquestioned political talents to benefit his country, the Democratic Party, New York state and his spouse. If, as is expected, Sen. Hillary Rodham Clinton becomes secretary of state, New York Gov. David Paterson could send her husband to the U.S. Senate.
This would not be unprecedented. John Quincy Adams was elected to the House of Representatives after leaving the White House and actually had quite a long and distinguished career there. Besides, Congress has interns too.