This has never been an easy metamorphosis. In fact, through most of our history, vice presidents have been held in such low esteem that they almost never dared to offer themselves as serious candidates for the top job and were rarely encouraged to pursue such a lofty ambition.
(Succeeding presidents who died in office was something else, however. That abrupt transition began in 1841 when John Tyler became the first unelected president - and was scornfully dismissed as "His Accidency" - and recurred periodically down to the mid-20th century when Harry Truman and Lyndon Johnson suddenly replaced fallen leaders.)
But presidents who had the good fortune to leave office alive and undefeated generally looked elsewhere for a worthy successor, often to members of their cabinets.
That's what Theodore Roosevelt did when he picked Secretary of War William Howard Taft to succeed him in 1908 and what Calvin Coolidge did when he gave his taciturn blessing to the candidacy of his Commerce secretary, Herbert Hoover, 20 years later.
Another rich pool of prospects favored by departing presidents was that of big-state governors. Think of Truman reaching out to Illinois Gov. Adlai Stevenson as his preferred candidate in 1952.
In contrast, a partial roll call of politicos who served as vice president during the first five decades of the 20th Century does not exactly set off lightning flashes of recognition.
Charles Fairbanks, James Sherman, Thomas Marshall, Charles Dawes, Charles Curtis and Alben Barkley were never in danger of being touted for the White House and, after leaving the nation's second highest office, they soon vanished even deeper into the mists of obscurity.
The first vice president of the modern era to break out of the rut and claim his right to succession was Richard Nixon.
Yet during his eight years as veep, he was regarded by his boss, Dwight Eisenhower, as little more than a political convenience, and a rather coarse one at that. Ike had no stomach for the vulgarities of partisan politics, and so he used Nixon as his attack dog so that he could be free to glide serenely above the battle, smiling and unsoiled.
Nixon's reward for doing the president's dirty work was to be treated with disdain. Even in 1960, when Nixon was mounting his own campaign for the White House and urgently needed his leader's support, Eisenhower couldn't resist an opportunity to belittle his two-time running mate.
At a news conference that year, when he was asked what ideas Nixon had contributed to his presidency, Ike replied: "Well, if you give me a week I might think of one."
With an endorsement like that to spuhim on, it's hardly surprising that Nixon was unable, in the '60 campaign, to graft Ike's enormous popularity onto his own candidacy.
But after losing to John F. Kennedy that year, Nixon went on to win the presidency in 1968, at least in part because by then he had broken free of Eisenhower's shadow and had established his own clear political identity.
The Democratic foe he defeated that year was Hubert Humphrey, another vice president who came to grief in his effort to capture the top prize.
In some ways, Humphrey's dilemma was the opposite of Nixon's in 1960. Instead of trying to wrap himself in the cloak of a highly popular president who didn't much care for him, Humphrey's delicate task was to put distance between himself and a beleaguered president who had squandered his popularity with his war policies in Vietnam.
By March of '68, when President Johnson announced he would not be a candidate for re-election, his own party was in open rebellion. Two antiwar senators - Eugene McCarthy and Robert Kennedy - had launched insurgency campaigns against his policies, and the tide of public opinion was shifting in their favor.
Johnson firmly pledged his support to Humphrey's candidacy, but in doing so he demanded, in return, absolute loyalty to his aggressive escalations of the war. That put the vice president in a terrible bind, which continued even after he won the Democratic nomination.
If he did not make some overture to the antiwar activists, he could not hope to draw their support and reunite his party. Yet at the same time, he was loath to take a stand against a fiercely strong-willed president who had a notorious reputation for bullying deputies who stepped out of line.
In the words of the late Richard Rovere, who was then the Washington correspondent for the New Yorker, Humphrey's problem was that "he had become a slave to a master who destroys his slaves" - as harsh an indictment of vice-presidential toadyism as has ever been written.
With barely more than a month to go before Election Day, Humphrey finally did liberate himself from LBJ's iron control with a speech that moved him much closer to the antiwar camp. And although he went on to narrow the huge gap between himself and Nixon, it was too late to close it completely.
More recently, there was Vice President George Bush's rather awkward attempt in 1988 to present himself as Ronald Reagan's natural heir.
Like Humphrey, Bush was known for his servile, puppy-dog devotion to the president he served. Yet that unwavering loyalty did little to endear him to many Reagan conservatives, who viewed him with disdain as a flaccid, watered-down version of their hero.
Thus, in launching his own campaign for the White House, Bush had to overcome that unflattering image, which, in various press accounts, was described as "the wimp factor."
It was an uphill struggle. As late as the summer of '88, polls showed the vice president trailing his Democratic oponent, Michael Dukakis, by 17 points. And indeed, if he had run against a stronger foe - such as the Kennedy of 1960 or the Nixon of '68 - Bush probably would not have been able to turn it around.
But Dukakis proved to be a weak candidate who waged an inept campaign, and that greatly helped the vice president surmount his own problems and put together the comeback he needed to win.
Which brings us back to Crown Prince Albert and the obstacles he must overcome in his quest to become the next Leader of the Free World.
Like Bush in '88, he is running against a successful governor who enjoys a strong, midsummer lead in the polls.
And like Nixon in '60, he is trying to draw unto himself some of the magic appeal of a president who, in terms of his policies and achievements, is still extremely popular. Bill Clinton's job-approval rating remains higher than that of any previous president in his eighth year in office.
Yet Gore's situation is also comparable to that of Humphrey in '68, for he needs to set himself apart from the reckless and deceitful Clinton, the one who was impeached for lying about his sexual fling with Monica Lewinsky.
In short, Gore must somehow manage to embrace with enthusiasm Mr. Clinton's record, while steering clear of the scandal that has left an indelible stain on his presidency. And no matter how you slice it, that won't be easy.
In one significant respect, the Republicans have already forced the vice president's hand. A central goal of the recent GOP convention was to nail Gore to the cross of Mr. Clinton's transgressions, and to judge from the vice president's rapid response, the strategy was a brilliant success.
Just three days after the Republicans adjourned in Philadelphia, Gore made the decision to select as his running mate Sen. Joe Lieberman, one of whose claims to distinction is that he was the first Democratic senator to denounce the president's behavior with Lewinsky as "disgraceful" and "immoral."
Talk about separating himself from the seamy side of his leader's tenure. The vice president couldn't have made his intention more clear if he had shouted from the rooftops his own stern disapproval of Mr. Clinton's sexual conduct in the Oval Office.
Nor is that Lieberman's only claim to distinction. On Wednesday night he will become the first Jew to be formally nominated for national office, and Gore has been justly applauded for that bold and unorthodox move - or Orthodox move, if viewed within the context of the senator's religious faith.
Now Gore must follow that up with other decisive actions, for there are many hurdles yet to be cleared.
The caterpillar has more skin to shed before he'll be free to butterfly his way to the White House. And that fascinating, change-of-identity process is what will engage so much of our attention over the next few days as the Democratic faithful assemble in Los Angeles to condemn the Republicans and all their works.