Oh, it's not entirely unlike that of an interim CEO brought in to turn around a failing company. Such folks might easily have to deal with many pissed-off constituencies (angry shareholders, unions not eager to make concessions, impatient creditors, perhaps even proud and cantankerous board members); they have only limited resources with which to manage the problem; and they're expected to be the source of major ideas (such as budgeting).

It's also them who frequently need to initiate actions that WILL anger large parts of their constituencies but may be better for the organization at a whole; and if it's a large company, he's probably not going to have time to micromanage everything so the selection of competent and honest staff becomes critical... too much to manage, and too many people feeding bullshiat in order to protect or enlarge their own little domains and blame everybody else for the trouble. Much the same way that with the seemingly ubiquitous belief among pressure groups that their own pet issue and viewpoint should be elevated to national policy, and that departments have their own reasons to deceive an administration over their own deficiencies and capabilities.

...and in both the case of the interim CEO and any president, they risk drawing flak not only for problems that they cause, but problems that they inherit. It's not exactly the fault of any recent president that consumers will happily buy cheap imported crap to the point that it makes economic sense to offshore manufacturing of low-end merchandise, for instance. And whoever the next president is, there's a pretty good chance that he won't have been a prime mover behind the Iraqi invasion given the political climate, but he'll certainly have to deal with the consequences -- regardless of whether they were caused by US stupidity, Iraqi decisions, the meddling of neighbors, or so forth.