Most mainstream press coverage of the debt ceiling issue still does not, I think, adequately capture the fact that the key reason the Obama administration doesn't want to negotiate over the debt ceiling is that an increase in the debt ceiling is not a concession by congressional Republicans.
Concessions, bargaining, and negotiation are very important to politics, and that's especially so in Madisonian systems with strong separation of powers. But the way that concessions, bargaining, and negotiation work are that Obama asks for something Republicans don't favor—a universal preschool program, say—and then Republicans counter with something they favor but Obama doesn't. Like if universal preschool is so great, Obama, why don't we pay for it by making Obamacare less generous and reducing federal spending on K-12 education and cutting other social safety-net programs for low-income people? Obama would probably say no to that, and then we'd have a standoff. Or maybe we'd have a back-and-forth of some kind. But either way, the point of the negotiation would be that Obama is asking Republicans to make a concession, so if he wants to get something done, he needs to make concessions in return.
But the debt ceiling isn't some pet Obama administration priority. There is a gap between the spending that Congress has instructed Treasury to undertake and the taxes that Congress has authorized Treasury to collect. Authority to borrow the money to fill the gap is necessary to legally dot the I's and cross the T's.
Granting it does not authorize any new spending, and failing to grant it does not cut spending. Obama is not asking Republicans for a favor, so he feels that they are not entitled to ask him for a favor in return. I think Republicans are on fair ground if they want to say that they got a favor from him in 2011, so they now want to make it a precedent that they get a favor for this. But honestly all that goes to show is that Obama's approach to this in 2011 was a mistake borne of political miscalculation. It's never been that "avoiding a chaotic and financially disruptive constitutional crisis" is some pet Democratic idea that Republicans are reluctant to agree to absent sweeteners.
Read more of Slate's coverage of the debt ceiling.