Look, I'm not really a political powerhouse, and I'm not much of a master tactician. For the most part, I agree with Hunter's opinion (and the opinion of a lot of people here) that Democrats need to own the fact that they, too, can be strong on defense, and they should have a Democratic Secretary of Defense.
However, I can think of one reason why Obama might want to have a Republican on board in that spot--specifically a Republican. I have no idea how useful it is, or if it's a good idea, or if it has any tactical merits at all, because, well... see previous paragraph. I'm terrible at this stuff. But it hit me out of the blue, so now I am hitting you guys in the Orange to see what you think.
TL;DR version: Obama wants a Republican as SecD because he's going to pull completely out of Afghanistan, in a big way, and it's the only way he's going to have Republicans involved in the withdrawal.
Longer version after the orange squidgy of penitent reflection.
I'm going to say two things right now:
1. I originally supported the invasion of Afghanistan (I did not support Iraq).
2. Afghanistan has turned into a clusterfuck.
Afghanistan turned into a clusterfuck largely because Bush really wanted to invade Iran, and moved all the shinies there, leaving the US military that was left behind to largely fend for themselves. Obama wanted to correct this, and he tried, but he's adopted some policies (drone bombings and administration-authorized assassinations, to name two) that have really poisoned our relationship with anyone who might be allies there. I'm absolutely positive there is context I'm missing and details I'm overlooking (again, see first paragraph) but that's how it looks to me.
So we're spending ridiculous sums of cash and throwing our soldiers into a meat grinder for something that's not working. Time to go.
Thing is, whether or not "time to go" is logical, there's going to be a hell of a lot of resistance to it. There are probably people in the military who think we need to stay, because they don't want another perceived Viet Nam (I know many people in the military who believe Viet Nam was a blow to America's credibility, and that it was the Democratic congress who was to blame, for pulling soldiers out of a winnable war). I also know veterans who served in Iraq who believe that this essentially happened with Iraq -- one specifically says that he feels he wasted his time over there, and that he saw gains made that he now feels were abandoned. So there will be institutional resistance from within the Military to getting us out of there.
There will also be resistance from every single damn Republican in the House and Senate, because it's Barack Obama who wants it done. If Barack Obama said tomorrow "I think breathing air is a fundamentally good thing" you would immediately have a House Resolution condemning the circulatory system and a bill introduced on the floor mandating the constitution be amended to require the removal of the lungs of every natural-born US Citizen.
So even if there are Republican Congressmen who believe that we need to get out of Afghanistan, they're going to pitch a fit and they're going to adopt the narrative that "once again, Democrats are weak on defense." I mean, they are. They are no matter what happens.
How do you counter that? Well if you have a Democrat who is Secretary of Defense, who would basically oversee that, you counter it with facts and a dose of reality and then you watch those silently drown in the echo chamber of nonsense that passes for political discourse these days, because it doesn't matter how competent Democrats are, the Narrative is the Narrative, and By God We Will Make Democrats Incompetent On Defense.
If you have a Republican who is Secretary of Defense, the truth is you're going to have to deal with the same shit. There will still be an echo chamber. There will still be people pinning it on Obama, and there will be some stick to that, because SecD works for the President. BUT... you'll also have a Republican sitting there who is actually organizing the withdrawal and giving the orders.
It doesn't matter whether individual Republicans support the withdrawal in Afghanistan. We'll never see that support actually translate into, you know, support... because opposing the Democratic administration is Job One. Putting a Republican in the SecD position is probably the only way to force a Republican to diligently participate in the withdrawal. And it might--though this is not guaranteed--blunt some of the echo chamber criticism because hey, look, there's a Republican talking to the press about the withdrawal.
You know, I can't say for sure that's the reason. I don't know if it's good tactics (seriously, see the first paragraph. I'm not being self-deprecating, the only way I understand politics is through satire, and what I think is satire sometimes turns out to be actually, genuinely true, and that confuses the hell out of me). I don't know if it will work. BUT I can sort of see someone thinking of this as a way of being a grownup while making sure the Democratic Party isn't the sole group to take the fall for it.
(By way of example: Before Carter was elected, many, many Republicans made statements saying that control of the Panama Canal needed to be handed over to Panama. Carter actually did it. The Republicans used it against him, gleefully, ever since.)
Anyway. Just a thought. I'm interested in yours.