We need to stop pretending this is about petty politics.
What does Hagel fundamentally affect when he becomes SecDef?
Not Benghazi bullshit. Not drone warfare. Not the withdrawals.
Two potential areas where Hagel can have a huge impact: on the responsible reduction of the Pentagon budget, and on American influence on the Israel/Palenstine conflict.
Of those two, Republicans themselves have signed on to Pentagon spending cuts.
So that really only leaves the issue of Israel/Palestine, where the GOP has a vested interest, and the Obama administration has strayed far from the "no light" policy that the GOP literally follows and many in the DNP diligently ape.
Hagel as SecDef fundamentally changes what Israel can leverage with the United States with the respect to doing pretty much whatever they want with Palestine and tell the world to "**** off if you don't like it, America's got our backs." With Hagel on board, that's not as much of a guarantee as it used to be. Israel finds itself in a really difficult position right now. The country under the Likud has effectively isolated itself diplomatically as report after report comes out about the squalor the vast majority of Palestinians are forced to live under, whether Israel feels it's justified or not.
America, honestly, is the only tether left to plausible international support. With an Obama/Hagel run Pentagon, Israel may have to choose over the course of the next four years: continue their current path and risk greater isolation, or swerve from the path towards apartheid.