He is — and also of his place in it. McConnell is atypically unconcerned, among senators, with his public profile. Even friends who attest to his dry wit and well-concealed sentimentality acknowledge a Man Without Qualities aspect to him: “He isn’t a jokester,” says Slade Gorton, the former Republican senator from Washington State and an old friend of McConnell’s. “He isn’t a party guy. He’s just — there. He’s just a fact of life.” Like a spy or a pinto bean, McConnell has used this blankness to his advantage, made it a carrier for designs greater than himself. His ascent in Republican politics came through his willingness to be the face of party prerogatives — fighting against campaign-finance reform during the Clinton and Bush presidencies, impeding a then-popular president’s agenda during Obama’s — that were distasteful to the general public, his shrugging willingness to play a villain when a villain was required.

But beneath this unconcern is a different kind of self-regard, a sense of himself as a historical figure in waiting. In his first Senate race, his campaign paid for a rare two-minute TV commercial tracing the arc of his life and work at a time when his elected career consisted of two terms as the judge-executive — a county-level mayor, essentially — of Jefferson County, Kentucky. When he was named Senate majority leader in 2014, and The Louisville Courier-Journal described him as the third from Kentucky, his staff called the paper, insisting he was the second and demanding a correction. (Earle Clements only filled in briefly for Lyndon Johnson after his heart attack.) At the McConnell Center that McConnell founded at the University of Louisville, his alma mater, there is an exact replica of the mahogany desk McConnell used as a junior senator, which was once occupied by Henry Clay, a fellow Kentuckian and one of the heroes of the 19th-century Senate, who engineered the Missouri Compromise. There is a bronze statue of Clay standing at the desk, but the brass nameplate on the desktop says “Mr. McConnell.”

But the particular way in which McConnell has always conceived of his own historicity is significant and unusual among contemporary Republicans. The Tea Partyers have their Mel Gibson-movie fantasies, the Trumpists their Pinochet-meets-“Die Hard” pastiches. But McConnell aspires to be not the bloody and maybe tragic hero in a revolutionary drama but one among a short list of undisputed masters of the machinery of American government, both essential to and dwarfed by the history of this machinery. Notably, the political philosopher he cites to the near exclusion of all others is Edmund Burke, the 18th-century Irish writer and Whig politician who essayed trenchantly against the French Revolution, and whose influence on 21st-century Republican politics you would have to squint very hard to make out.

This vision is also unmistakably senatorial. McConnell recognized his future in politics by high school and narrowed his ambitions to the upper chamber by the time he graduated from college; on his law-school applications, according to his authorized biographer, John David Dyche, one of his professors wrote that McConnell ‘‘will be a U.S. Senator.” “I was running for the Senate in ’84 from the moment I was sworn in as county judge on Jan. 1, 1978,” McConnell once said — and he has never aspired to anything outside it. “I think most senators look in the mirror and think they hear ‘Hail to the Chief’ in the background,” Terry Carmack, who has worked for McConnell on and off since his first Senate campaign, told me. “But he always wanted to be in the Senate.” And from early in his Senate career, McConnell later wrote, “I wanted to one day hold a leadership position in my party, helping to call the plays and not just run them.”

The Senate majority leader wields an elusive kind of power. The position, which dates back to the 1920s, is as paradoxical as the institution, which is given the authority to make great changes but also given as many tools to impede those changes as to enact them. To the Senate’s defenders, this is the “cooling saucer” of George Washington’s probably apocryphal explanation; to its detractors, it is more like an unreleasable parking brake on progress, never truly succeeding at holding back the future but ensuring that the country’s arrival at it will be as delayed and frictional as possible. At the turn of the 20th century, the Senate proved ineffectual in regulating railroads and banking. It failed to grasp the severity of the Depression until Americans had endured its hardships for years, offering only the meekest of remedies until Franklin D. Roosevelt forced lawmakers to do otherwise. Isolationists in the chamber impeded efforts to check Adolf Hitler’s advance in Europe; Southern conservatives were effective enough at delaying legislative action on civil rights to prompt the oft-quoted observation of William S. White, The Times’s congressional correspondent in the 1950s, that the Senate was “the South’s unending revenge upon the North for Gettysburg.”

This began to change under the leadership of Lyndon Johnson in the late 1950s, but especially under Mike Mansfield, the Montana Democrat who served as majority leader from 1961 to 1977, longer than anyone before or since. Though he enjoys a lesser profile than Johnson, Mansfield is more admired within the Senate by Democrats and Republicans alike, as a magnanimous and gentlemanly conductor of the upper chamber’s fractious orchestra. “He treated everyone alike, without regard to politics or seniority,” Ted Stevens, the Republican senator from Alaska, once said. It was on Mansfield’s watch that the Senate passed the Civil Rights Act of 1964, enacted Medicare, forced the resignation of Nixon without conviction and passed an array of post-Watergate reforms to the government and the Senate itself. Senators talk about Mansfield the way jazz musicians talk about Charlie Parker: He is the figure whose accomplishments they are doomed to be judged against forever, even as the context in which those accomplishments were possible recedes irretrievably into the past.

McConnell first arrived in the Senate in what was arguably the most momentous year of the Mansfield era, 1964, as an intern for John Sherman Cooper. A moderate-to-liberal Republican, Cooper was then helping round up Republican votes for what would become the Civil Rights Act. McConnell, who supported civil rights as a college student, has spoken reverently of attending the signing ceremony for the Voting Rights Act in the Capitol Rotunda, at Cooper’s invitation, the following year. In his telling, it remains the platonic ideal of legislation, passed with the support of majorities of both parties.