To select a member of the Jewish faith - and an Orthodox Jew at that - was a bold and progressive move, yet another decisive step to break down the barriers of ethnic bias in our body politic.
And I naturally assumed that Jews, regardless of party, would greet the news with pride and satisfaction, in much the same way that in 1960 Irish Catholics, regardless of party, had greeted the news of John F. Kennedy's election with pride and satisfaction.
So I was somewhat surprised by the apprehensive reaction of a Jewish friend of mine, a longtime political observer whose judgment I respect a great deal. His main concern was that the choice of Lieberman will provoke a muted - but significant - backlash.
"There's still a lot of anti-Semitism out there, simmering beneath the surface," he asserted.
Yet when I pressed him, he admitted he was basing that view mainly on instinct and feeling, and had no solid empirical evidence to support it.
But when I countered by saying that the polls revealed an overwhelmingly favorable response to the Lieberman candidacy, he reminded me that polls that touch on matters of prejudice or intolerance are notoriously suspect.
And he was right about that. When George Wallace was running for president as a race-baiting protest candidate, polls invariably showed him getting a substantially lower percentage of votes than he would actually receive on Election Day.
That's because many Wallace supporters did not want to give pollsters the impression they were biased. But once inside the voting booth, they only had to answer to themselves.
"If the Democrats win, then I'll be proven wrong," my friend said. "But if that ticket loses, then Lieberman could become the scapegoat and that would be a real setback for future Jewish candidates."
I told him I didn't share his pessimism, but the more I thought about it, the more I found his comments disturbing because they reminded me of an interview I had back in 1984 with the late Tip O'Neill, who was then Speaker of the House.
At one point he began talking about John Kennedy - one of Tip's favorite subjects - and the next thing I knew, he was recalling the 1956 Democratic National Convention in Chicago.
That was the one where the nominee, Adlai Stevenson, waived his right to select a running mate and left the choice up to the convention, an unexpected move that first stunned and then electrified the delegates. What followed was a spirited, even frantic scramble for the vice presidential nomination.
The eventual winner on the second ballot was Tennessee Sen. Estes Kefauver. But two of his biggest rivals were his fellow senator from Tennessee, Albert Gore - yes, the father of this week's nominee - and the 39-year-old Kennedy, then in his first term as a senator from Massachusetts.
In fact, Kennedy came very close to gettng the votes he needed to become Stevenson's running mate in that '56 campaign.
"Which would have been a disaster," Tip O'Neill said in our conversation 28 years later. "No matter who ran with him that year, Stevenson was going to get clobbered by Ike, and if that landslide had happened with Jack on the ticket, they would have blamed him - and his religion.
"He would have been damaged goods, and so forget about 1960. There's no way he would have been able to run for president that year. And to take the larger view, we would have been looking at the Al Smith thing all over again because my guess is it would have taken years - even decades - before either party would run the risk of nominating an Irish Catholic for president.
"And that," O'Neill added in a characteristic flourish, "would have been a great loss for civilization."
The reason O'Neill brought up the 1956 convention was because of what was happening with the Democratic Party when our interview took place in the early autumn of 1984.
A few weeks earlier, the party's presidential nominee, Walter Mondale, had selected as his running mate New York Rep. Geraldine Ferraro - the first woman to be so honored.
The general reaction to Mondale's choice was strikingly similar to all the praise showered on Gore last week when he made the Lieberman announcement. But by the time of my interview with O'Neill, the Speaker was convinced that the Mondale-Ferraro ticket was in deep trouble.
"I'm afraid we're going to lose this election, and probably lose it big," he said in a sorrowful tone. "And that's going to be very tough on Gerry and for the whole cause of someday electing a woman president."
Tip O'Neill was, as usual, right on target. The Mondale-Ferraro ticket was buried in a huge landslide as President Ronald Reagan cruised to a second term. And since then, neither party has shown much enthusiasm for nominating a woman for national office.
So Joe Lieberman will be carrying plenty of baggage into the fall election. If the Democrats are decisively beaten in November and fingers start pointing at Gore's running mate, it could be very bad news for future Jewish candidates who aspire to national office.
I wish I could "say it ain't so, Joe" - but the historical evidence suggests otherwise.