Why wasn't backlash a concern? Is Obama going out of his way to get people to hate him on the way out?
My understanding was that both Obama and Biden viewed securing Bergdahl's release being of paramount importance. This was also the view of the majority of the President's advisors within the Administration (in the defense department and CIA as well).
The idea was that he shouldn't be a prisoner to the Taliban, and beyond that, he may have been beheaded on camera (not ISIS style, but nonetheless).
Clinton worked to secure his release, but supposedly she was not onboard with the cost. Which, I'm told, was entirely due to the potential for political backlash (this really is the edge of a much larger issue tangentially related to this topic) which goes to Q-Tip's point.
Ultimately, Obama went with his advisors, including CIA, State (excluding Clinton - but including her staff), the veep, and the joint chiefs recommendation.
Obama, at this point, honestly gives two shits about politics or the next election... to the dismay of many Democrats, particularly Bill Clinton more so than anyone else. They are furious with him right now, as they tend to be.
p.s.
As always take this with a grain of salt, it's not first party and the person who relayed this was not "in the room" so during these discussions but was "around."