If Obama does pick people for top Cabinet positions from across the aisle, it will also not be unprecedented.
For instance, before taking office in 1961, President-elect John F. Kennedy tapped Republican Clarence Douglas Dillon for Treasury secretary. Kennedy also selected Robert McNamara, a liberal Republican who was then president of Ford Motor Company, to be his secretary of defense.
More recently, Republican William Cohen was sworn in as defense secretary in 1997 under Democratic President Bill Clinton. When he took office in 2001, Bush appointed Democrat Norm Mineta, Clinton's commerce secretary, to be secretary of transportation.
"Having a couple Republicans in the Cabinet does not guarantee greater effectiveness, but it may open communication channels," said Darrell West, vice president and director of governance studies at the Brookings Institution.
Still, Hess warned that Obama should not make picks that could be divisive by tapping extremely partisan people.
"Be cautious, Mr. President, about these appointments," Hess said.
"There is no doubt that I think people want to know who's going to make up our team, and I want to move with all deliberate haste, but I want to emphasize deliberate as well as haste," Obama said Friday at a press conference. "And I think it's very important in all these key positions, both in the economic team and the national security team, to -- to get it right and -- and not to be so rushed that you end up making mistakes. I'm confident that we're going to have an outstanding team, and we will be rolling that out in subsequent weeks."
Still, many Washington insiders said making Republican picks for Cabinet posts won't be nearly as critical as fostering a bipartisan climate in Congress. What matters most, they said, is to have friends on the other side of the aisle on Capitol Hill.
"That's what it comes down to -- in this city at least -- when you talk about bipartisanship," Hess said.
Former White House chief of staff Ken Duberstein, who served under President Ronald Reagan, also said staff selection would be just as critical, if not more critical, than Cabinet picks.
"It's the White House staff – starting with chief of staff and then going out – that really has the ear of the president of the United States," Duberstein said, cautioning that Cabinet members get trapped representing their special interest groups to the president rather than the reverse. "That's the way it really works."