WASHINGTON — Six years after Joe Lieberman presented Jewish Democrats with an unprecedented triumph, he may pose an intractable dilemma.

If the U.S. senator from Connecticut loses an Aug. 8 primary to a come-from-nowhere challenger, Jewish Democrats may have to choose between loyalty to the party and the man who made history in 2000 as the first Jew nominated to a national ticket.

Lieberman announced his decision this week to collect enough signatures for an independent run if he loses the primary in his bid for a fourth term. That’s a sign that he perceives a real threat from Ned Lamont, a millionaire whose challenge focuses overwhelmingly on Lieberman’s support for the Iraq war.

“I’m going to be there on Nov. 7 one way or another,” Lieberman told The Associated Press after his announcement.

The question for Jewish Democrats is where will they be.

“It does present a dilemma,” said Steve Grossman, a former chairman of the Democratic National Committee.

“If you consider yourself first and foremost part of the pro-Israel community, you will stick with Joe Lieberman,” said Grossman, who also is a past president of the American Israel Public Affairs Committee. “If you’re so overwhelmingly convinced that ending the war as soon as possible is of paramount importance, I could understand why you would find Joe Lieberman a candidate you could no longer support.”

Lamont’s campaign says the issue isn’t so clear-cut, insisting that he, too, is focused on Israel.

“Israel’s security is a topic that is very important to Ned,” said Liz Dupont-Diehl, the campaign’s communications director. “He has a lot of respect for Israel.”

She said Lamont had met with a number of Jewish leaders. Jewish officials, however, say they haven’t sensed any outreach.

“I don’t think he’s spoken out effectively to things the mainstream Jewish voters feel,” said Richard Greenfield, publisher of the Connecticut Jewish Ledger.

On Lamont’s Web site, the single foreign issue addressed is Iraq. Israel merits a passing mention in that context: “Israel is no safer” since the Iraq war, the site says.

If Lieberman does end up losing the primary and running as an independent, it would split Jewish voters, said Steve Rabinowitz, a strategist who advises Democrats and Jewish groups.

“A lot of Jewish Democrats will support the Democratic nominee because they’re Democrats, but there will be support for the icon Joe Lieberman,” he said.

Grossman said he’s supporting Lieberman.

“I don’t criticize those who can’t support Joe Lieberman because he no longer represents the views of progressive Democrats. But there has not been a greater champion of Israel and the well-being of the Jewish people,” Grossman said.

It’s unclear how many Jewish Democrats share that view. Jewish fund-raisers canvassed by JTA said they favored Lieberman — even those who profoundly disagree with him on Iraq.

But an internal Democratic poll of Connecticut Jews sees Lamont leading by 50 percent to 41 percent, JTA has learned. The sample was small, but the results were a dramatic departure from the 90-plus approval rating Lieberman scored among Jews after Al Gore named him as his running mate in 2000.

Connecticut Jews make up 111,000 of the state’s 3.4 million people, or a little more than 3 percent of the population, according to the Jewish Virtual Library.

Lieberman’s backers attribute the shift to opposition to the Iraq war. Jewish opposition to the war has always outpaced general opposition.

“I find the behavior of a large segment of the Jewish community to be reprehensible and outrageous,” said John Droney, a former chairman of the state party who is advising Lieberman to run as an independent. “When he’s in trouble like this, they all ought to rally to him. It’s too bad that you have to listen to an Irish-American to realize that you’ve got to support your own home cooking.”

Lamont, a cable TV millionaire, has closed the gap significantly by battering Lieberman on his support for the war and his friendliness to President Bush.

In a May 2 Quinnipiac poll of likely Democratic voters, Lieberman enjoyed a 65 percent to 19 percent lead. In a June 8 Quinnipiac poll, the lead had dwindled to 55-40. A recent Rasmussen poll showed Lieberman clinging to a six-point lead.

Lamont’s supporters ran a float in a July 4 parade in Hartford that featured a caricature of the kiss Bush bestowed on Lieberman after Bush’s State of the Union address in January. A bumper sticker on the float read, “Just (politically) married,” and supporters shouted, “Joe Must Go!”

Much of the impetus comes from Democratic bloggers furious with Lieberman for supporting the war. MoveOn.org, a clearinghouse for antiwar activists, backs Lamont.

“There’s no question about it; Lieberman is running a two-phased campaign,” said Rabbi Menachem Genack, an Orthodox Union official who lives in New Jersey. “He has to run against a nationwide coalition of bloggers and also against Lamont.”

Voters should take into account Lieberman’s solid record on a host of issues other than Iraq, including support for labor protections and health reform, said Sue Turnbull, the Jewish vice chairwoman of the Democratic National Committee.

There already are signs of a split in the party. Sen. Hillary Rodham Clinton (D-N.Y.) said she backed Lieberman, but added that she wanted to “be clear that I will support the nominee chosen by Connecticut Democrats.”

By contrast, Senate minority leader Sen. Harry Reid (D-Nev.), and Sen. Charles Schumer (D-N.Y.), who heads the Democratic Senatorial Campaign Committee, refuse to comment on whom they will support after the primary.

Jewish Democrats should be wary of Lamont, pro-Israel fund-raisers said.

“The people who are doing this have no concern for Israel or issues of concern to the Jewish community,” said Dr. Ben Chouake, president of Norpac, a nonpartisan, New Jersey-based political action committee. “This is an example of an extreme left that really is looking to put a scalp on their wall to show that they have power.”

Democrats in general are missing the bigger picture, said Alan Solomont, a Boston-based Jewish fund-raiser who headed funding for John Kerry’s 2004 bid for the presidency.

“The left in our party who favor a different approach to Iraq are turning their fury on Joe in a way that I don’t think is particularly helpful,” Solomont said. “I differ with Lieberman on Iraq but I don’t think Democrats can afford to break ranks right now in the face of extreme right-wing control of the entire federal government.”

Democrats hope to win back one or both houses of Congress in November. But Marvin Lender, a Connecticut entrepreneur who chairs the Israel Policy Forum and has backed Lieberman for decades, says a Lieberman loss would send an unsettling message to Democrats who hope to win.

Ultimately, when it comes to Jewish support, Rabinowitz said, Lieberman might be a victim of his success: Now that a Jew has placed on a national ticket, Jews no longer feel the need to reflexively support every Jewish candidate.

“We have achieved as a community virtually every level of acceptance politically in this country,” he said. “So as much pride as there has been, Jews are way past the point where we knee jerk for the Jewish candidate.”

Washington Bureau Chief Ron Kampeas contributed to this story.