One of the things that I think Rumsfeld did perfectly was handle the question of a possible resignation. In particular, one senator asked him, in essence, if he would step down if his presence was a hindrance regarding Iraq. And he simply answered "Yes".
That spoke volumes about him valuing getting the job done more than valuing being right.
And I hope he means it because it may come to it (though I sincerely hope not).
At first glance, the call for resignation is absurd. Rumsfeld almost certainly knew nothing about what was happening at Abu Ghraib, and, as he rightly points out, he should not be expected to know the details of all 3,000 odd current court martial investigations. He has plausable denaibility in spades. Some would call on the principle of "The buck stops here", here being in this case Rumsfeld. That would be true if the we lost the Iraq war, or if the entire Iraq reconstruction effort fails. But not for the administration of a prison, or even for the administration of all the prisons. That buck stops somewhere lower on the chain of command. (Where? I have no idea--any ideas?)
So why might a resignation be necessary? Because he is responsible for the entire Iraq reconstruction, and if it fails horribly, the buck stops with him. He must therefore do whatever it takes to ensure that the Iraq reconstruction goes well, regardless of his actual complicity in the abuses at Abu Ghraib. So he might be forced to step down if the people if Iraq end up identifying him (no matter how falsely) with the abuses at Abu Ghraib.