And over the past three decades, most Democratic nominees failed to pass the test. In one way or another, they squandered the golden opportunity to give their candidacies the boost needed to put them on the road to victory.
Few moments in modern Democratic history were more frustrating and suicidal than the last night of the 1972 convention.
It was not so much that the nominee, George McGovern, gave a poor speech. His address, built around the theme and recurring phrase, "Come Home, America," had enough rhetorical flourishes to make a positive impression on a national television audience.
But he was betrayed by his own delegates who, during the roll call for the vice presidential nomination, engaged in a prolonged spree of self-indulgent frivolity that pushed the balloting well beyond prime time.
Which meant that McGovern didn't deliver his speech until the wee hours of the morning - prime time only in Guam. His campaign never recovered.
Jimmy Carter had better luck in 1976 and he began his remarks by reciting the line he had used time and again to introduce himself during the early primaries when he was an obscure, long-shot candidate: "My name is Jimmy Carter, and I'm running for president."
That warm and folksy opening set the tone for the entire acceptance speech, and it put Carter on the winning track to the White House.
But four years later, when he ran for re-election, his performance at the convention was a big disappointment. In responding to attacks on his leadership as president, Carter adopted a tone that was much too defensive, even apologetic. ("I'm wiser than I was four years ago.")
And he committed embarrassing gaffes. In a tribute to the recently deceased senator from Minnesota, Hubert Horatio Humphrey, the president misidentified him as "Hubert Horatio Hornblower. . . er, Humphrey."
Thanks in large part to Carter's bumbling speech, his Republican challenger, Ronald Reagan, was able to seize the initiative and he went on to a landslide victory in November.
Then in 1984, it was Walter Mondale's turn to give an acceptance speech that sent his campaign careening off the rails. The most memorable part of his address was his declaration that if elected, he would urge Congress to raise taxes.
Such a stand was no doubt fiscally responsible, even courageous, but it was also political suicide. From that moment on, Mondale's candidacy was doomed and Reagan was easily elected to a second term.
Going into the midsummer conventions in 1988, the Democratic candidate, Michael Dukakis, enjoyed a double-digit lead in the polls over his Republican foe, Vice President George Bush.
But the centerpiece of Dukakis's acceptance speech was his assetion that the '88 contest would be "about competence, not ideology." What he failed to understand is that triumphant presidential campaigns are more about leadership and vision than they are about either competence or ideology.
Dukakis's technocratic emphasis on competence was an early signal that the first Greek-American to become a presidential nominee would be running with all the verve of "Zorba the Clerk," as he came to known during that campaign.
By way of contrast, Bush's acceptance speech at the Republican convention that year was filled with such bright and punchy lines as "a kinder, gentler nation," and "a thousand points of light" and the infamous "read my lips" promise not to raise taxes.
That particular pledge would come back to haunt Bush when he was in the White House, but in the short term it clearly helped give him the impetus he needed to overtake Dukakis and win the election.
The Democratic losing streak came to an end with Bill Clinton's acceptance speech in 1992. For millions of Americans, it was the first time they saw Clinton in full cry on a podium and they had ample reason to be impressed.
Full of energy, compassion and confident resolve, his address was in almost every respect a state-of-the-art performance, right down to the closing, rather sentimental admission that "I still believe in a place called Hope."
Thus was ushered in the Clinton era in American politics, a two-term stretch in the White House that is now drawing to a close.
So will his hand-picked successor, Al Gore, be the one to succeed him? Well, the reaction to his speech Thursday night will go a long toward determining that.
Over the next few days that reaction will set in and harden like ice on a pond, and once it does - if history is an accurate barometer - we should then have a fairly clear idea of what kind of shot the vice president has for victory in November.