This is true whether one considers the powers of his office, or the symbolic role the office-holder is called to play as the efficacious sign of national unity.
Let these two aspects of consideration correspond roughly and respectively to the tasks of governing and reigning.
NB, I say, "roughly," for a reason: sometimes, official presidential authority is used to reign, as when the POTUS issues a Thanksgiving Day proclamation; at other times, such as the Coal Strike of 1902, when Theodore Roosevelt used the prestige of the office to bring what had become an ungovernable situation back under control, the powerful symbolism attached to or inherent in the office of POTUS is used to govern.
In other words: when you have a monarchy, elected or otherwise, and not a diarchy, the king (call him the POTUS) will sometimes govern by reigning and sometimes he will reign by governing.
President Obama was reigning in Tucson as the nation's "mourner-in-chief" - and he acquitted himself admirably.
He was also, and contemporaneously, governing.
Our nation is now like a ship, the crew of which is on the verge of mutiny: the officers (Congress) are incompetent at best, venal at worst; the crew is divided over whether to trust the captain, whose past service is storied, but whose recent performance has been aloof, retiring, and when present, heavy-handed.
The POTUS seized a moment of national shock and suffering, and called the crew to order, not by scolding, not by blaming, but by reminding them of their past glories, and calling on them - on us - to believe ourselves yet capable of that authentic national greatness, which is grounded in prudent regard for basic human goodness.
Senator McCain put the matter thusly:
The president appropriately disputed the injurious suggestion that some participants in our political debates were responsible for a depraved man's inhumanity. He asked us all to conduct ourselves in those debates in a manner that would not disillusion an innocent child's hopeful patriotism. I agree wholeheartedly with these sentiments. We should respect the sincerity of the convictions that enliven our debates but also the mutual purpose that we and all preceding generations of Americans serve: a better country; stronger, more prosperous and just than the one we inherited.In other words, POTUS was reminding the nation of (even as he wrestled with) a profoundly patriotic and quintessentially American idea: that America (the conceptual space that informs our nationhood) is at once good, and in its embodiment, not (yet) good enough - not (yet) as good as it should be - so he was calling us to the kind of moral improvement in which the possibility of America is proved.
We Americans have different opinions on how best to serve that noble purpose. We need not pretend otherwise or be timid in our advocacy of the means we believe will achieve it. But we should be mindful as we argue about our differences that so much more unites than divides us. We should also note that our differences, when compared with those in many, if not most, other countries, are smaller than we sometimes imagine them to be.
I disagree with many of the president's policies, but I believe he is a patriot sincerely intent on using his time in office to advance our country's cause. I reject accusations that his policies and beliefs make him unworthy to lead America or opposed to its founding ideals. And I reject accusations that Americans who vigorously oppose his policies are less intelligent, compassionate or just than those who support them.