I can see a case for a GOP as Secretary of Defense. First though...the case against: Obama doesn't NEED a GOP in that position. Obama "owns" defense/foreign affairs, to an extent no Democrat has since JFK, if not FDR. Obama doesn't need the "political cover" of a GOP in this position. And, Obama's and the Democrats' "ownership" of this issue has been hard and well earned. It may be a little early, to let the GOP back in this door.
On the OTHER hand.....we've seen considerable evidence already - from his first term - that Obama is intending a rather considerable and in some ways, "radical" revision and overhaul of our traditional defense posture and framework. Polling of the middle of the electorate, suggests that the prospects of our downsizing, re-sizing, or whatever, makes people a little nervous. I conclude that, from polling suggesting that "the people" aren't comfortable with the prospect of "the sequester" taking a chunk out of defense. So.....IF the Obamans ARE contemplating what might be perceived as "radical" change, it would definitely be worthwhile to be able to present that the changes had the "buy in" of not just someone with Hagel's "chops", but a GOP to boot.
It's a "trust" thing. The people didn't trust Reagan to reform welfare. They did trust Clinton to do so. At this point, "the people" obviously trust Obama as to defense. But, they may not trust a Democrat quite so much, when it comes to cutting or reforming defense.