I don't think this needs to be settled ahead of time. If we shut off the tap of infinite student debt funding I guarantee the universities will magically discover what administrators and departments are dispensable quicker than you can imagine.
Same with government. Government waste is bad? Of course! Trim unnecessary government spending and pork barrel? Yes!! And which branches and positions should we cut? The Right Ones!! [cue nothing actually happens]
Shut off the money first. Some of the universities will make their cuts in academic and research departments. That's fine. I don't expect we'll hear too much from them after a while. Good riddance.