If you believe the latest poll, American Jews have lost that lovin’ feeling for Joe Lieberman and probably never had it for the Rev. John Hagee.

Therein lies the rub: Hagee’s representatives do not believe the results, saying the poll — commissioned by J Street, the new left-leaning pro-Israel lobby — relied on skewed questions. As for Lieberman, the Democratic-turned-independent U.S. senator from Connecticut is not disputing the findings, but says he pays little attention to polls.

According to the poll, which has a margin of error of 3.5 percent, Lieberman scored an unfavorable rating of 48 percent, compared to a favorable rating of 37 percent. Hagee, a leading right-wing Christian Zionist whose endorsement of Sen. John McCain (R-Ariz.) triggered a firestorm earlier this year, fared even worse: The pastor registered a 7 percent favorable rating, while his unfavorable rating came in at 57 percent.

The poll, based on interviews with 800 Jewish respondents between June 29 and July 3, comes amid heightened Democratic criticism of Lieberman’s support for Hagee and his pro-Israel efforts. J Street and Jewish liberal activists and bloggers waged a campaign urging Lieberman to skip Hagee’s Christians United for Israel conference in Washington last week. On the eve of the event, Americans for Peace Now also asked Lieberman to take a pass. Despite the mounting pressure, Lieberman opted to follow through with his appearance and speech.

J Street, which advocates a pronounced role for the United States in the peace process that would at times encompass pressure on Israel, says the results — particularly regarding Hagee, who opposes any U.S. pressure on Israel — underscore its argument that most American Jews reject Hagee’s view and the idea of working with him.

“When presented with both sides of the debate over U.S. policy in the Middle East, American Jews strongly favor the United States using its leverage to help resolve the Arab-Israeli conflict,” the group said in a statement.

According to J Street’s executive director, Jeremy Ben Ami, part of Hagee’s problem with American Jews is that he brings a strong religious sensibility to his politicking.

CUFI’s executive director, David Brog, said that such comments reflect a fundamental misunderstanding of Hagee’s mission.

Hagee’s theological musings have little to do with why he promotes support for Israel, Brog said, adding that his efforts instead are underpinned by sympathy for a fellow democracy facing the threat of radical Islamist terrorism.

Half of the respondents to the survey were asked, in one series of questions, whether various alleged facts and statements were “convincing reasons to oppose forming alliances” with Hagee and CUFI. Between 59 percent and 63 percent of the respondents said it was convincing to oppose such ties based on claims that Hagee sees supporting Israel as a way to help “bring Armageddon and the second coming of Christ,” opposes U.S.-backed peace initiatives because he wants to prevent an Israeli withdrawal from the West Bank, and has said that liberal Jews who disagree with his opposition to abortion and homosexuality are “not driven by the word of God.”

The number jumped to 81 percent when a subset of 400 respondents were told: “Reverend Hagee’s derogatory comments toward women, African Americans, Catholics and gay people led the top Reform rabbi in America top publicly call on American Jews not to form alliances with Hagee.”

Hagee’s supporters took issue with questions, arguing that they distort his record.

The pastor has, in fact, repeatedly disavowed End of Days theology, and alienated some evangelical allies by arguing that Jews do not need to convert to undergo salvation. The survey questions also failed to note that the pastor subsequently apologized or clarified remarks that have in the past offended gays, African Americans and Catholics.

Lieberman’s staff did not dispute the results, but suggested they were inconsequential for a senator who is enjoying his maverick reputation since leaving the Democratic Party in 2006.