What kind of job is president of the United States? The Constitution created it as an elective office, whose occupant serves at the pleasure of Americans who vote. But it is also the heart of a mighty enterprise, so much so that critics have bemoaned the growth of the “Imperial presidency.” Recently “King Obama” has become a refrain from his critics on the right.

The uneasiness over presidential authority isn’t just a product of current political polarization, or even of America’s global dominance since last century. In fact, it runs so deep in the history of the republic that it was the subject of the very first dispute between the House and the Senate. Before the first federal Congress took up the issue of amendments or settled on national financial instruments, it argued over a question whose answer we now take for granted: What should the president be called?

The great presidential title debate is little-examined today, and rarely comes up in history books. But it gripped the nation in 1789, in newspapers and in legislative sessions. Suggestions for a title ranged from the plain to the royal—from the simple “President” to “His Majesty” or various forms of the frequently used “Highness.”

The numerous titles under consideration at the time offer a window into the novel circumstances of America’s situation in 1789, as a young and increasingly democratic nation in a world where most power still resided with monarchs. And, perhaps even more relevant today, the debate also illustrates the warring impulses at work in what we really want from our leaders...