The effort to slander Chuck Hagel and to torpedo his potential nomination to be secretary of defense has reached such intensity that there is now much more at stake in this nomination than just who will be running the Pentagon over the next four years. Robert Merry in these spaces has portrayed well the sordidness of the calumny-flingers who make little effort to hide their main reason for going after Hagel, which is that he does not believe in subordinating U.S. interests to the wishes of the right-wing Israeli government and its American backers. Those in the anti-Hagel campaign who try to make it look as if there are non-Israeli reasons to shoot him down make arguments that move from the sordid to the ridiculous. The Washington Post's editorial on the subject is a good example. It tries to portray the former Republican senator from Nebraska as some kind of leftist peacenik, because he suggests there is some trimming that could usefully be done to U.S. defense spending (which is greater than the next 14 biggest military spenders—friends and foes—put together, and is the highest in inflation-adjusted dollars that it has been since World War II) and expresses skepticism about going to war against Iran (which the Post's editorialists acknowledge they have also expressed skepticism about, but that doesn't stop them from portraying the skepticism as somehow a point against Hagel). For a more thorough dismantling of this absurd editorial, see Andrew Sullivan's exegesis of it.
To the extent the placing of Hagel's name in the kind of unofficial nomination it is in right now was the result of deliberate balloon-floating by the White House, it is hard to see exactly what the White House thought it was doing. Making the nomination official and letting Hagel speak for himself would do a lot to puncture the falsehoods and smears about him. Maybe letting his name get out as the leading potential nominee was less a calculated act than plain old sloppy leaking. If one wants to give the White House more credit than that, one might postulate that it floated the name so the opponents would have a chance to discredit themselves so much through the sheer outrageousness of their arguments that they would not only lose this political battle but also be weaker in later ones. That way the president might get not only the secretary of defense he wants but also some more running room on issues such as the Iranian nuclear program and the Israeli-Palestinian conflict.
There is some valid logic to that. But such bold political jiu-jitsu does not seem to be this president's usual style. He is more likely to be thinking in the customary way, as discussed by Peter Baker in the New York Times, about conserving political capital, picking one's fights carefully, and keeping in mind all the other issues he may have to fight about (and he just got another one: gun control).