This frequently happens with secretaries of Defense, and it has been of benefit to the administrations that have done it. FDR picked a Republican, Henry Stimson, to be secretary of War in 1940, and that meant that the war — and the war’s casualties — became a bipartisan matter instead of fodder for partisan attacks. President Obama retained George W. Bush’s Defense secretary, Robert Gates, for most of his first term. He replaced Gates with another Republican, Chuck Hagel, in that position.
Having a Defense secretary from the other party makes war bipartisan, and reassures members of the opposition that the powers of the sword aren’t being abused. Likewise, naming an attorney general from the opposite party would tend to make the administration of justice bipartisan, and would provide considerable reassurance, as Holder’s tenure in office emphatically did not, that the powers of law enforcement were not being abused in service of partisan ends. In an age of all-encompassing criminal laws, and pervasive government spying, that’s a big deal.
With only a couple of years left in office, President Obama is inevitably looking to his legacy. Beginning a tradition of nonpartisan administration of justice would be a legacy indeed.