“Now some Jewish millennials are leaving the party,” he said. And the cable news network had found at least one: Elizabeth Pipko, a former Trump campaign staff member who last appeared on the network in January, when she was presented as a model who was a “secret Trump supporter.”

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But now she was there as the spokeswoman for “Jexodus,” a group formed for pro-Trump Jewish people. Pipko’s appearance soon drew a tweet from President Trump, who quoted her assertion that Jewish people were leaving the Democratic Party because of supposed anti-Semitism and “anti-Israel policies.”

On Friday, the president briefly returned to the topic on Twitter.

But polling data and experts interviewed by The Washington Post do not show a Jewish exodus from the Democratic Party in the Trump years. They show a demographic group that continues to vote at exceedingly high rates for Democrats — as it has for decades. That number actually ticked up when Trump was elected, with 71 percent voting for Hillary Clinton and only 24 percent voting for him in 2016.

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“This is something people have talked about for decades,” Matt Boxer, a professor at Brandeis University who has studied Jewish political involvement, said of the push for Jews to leave the Democratic Party. “But there’s no evidence when you look at survey data.”

Pipko did not immediately respond to a request for comment.

The Fox segment punctuated a second week of controversy over remarks made by Omar this month that some found anti-Semitic. Omar, already in the political crosshairs for a tweet putting forth the idea that money from pro-Israel lobbyists influenced the workings of Washington, had later criticized some pro-Israel efforts as a “push for allegiance to a foreign country."

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Democrats were among the first to rebuke her. But Republicans, lead by Trump, have used the opening to try to paint the Democrats as a party that is hostile to Jews and the interests of Israel.

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But Jewish voters have voted overwhelmingly for Democrats for decades; the numbers during presidential elections are particularly stark. About 80 percent of Jewish voters have cast their ballots for the Democrat in elections dating back to 1992, when George H.W. Bush received a meager 11 percent during his unsuccessful reelection campaign, according to statistics compiled by the American-Israeli Cooperative Enterprise.

The number of Jews voting Democrat dipped slightly in 2012, when 30 percent voted for Republican Mitt Romney. But it reverted back to the norm of recent years in 2016; only 24 percent of Jewish voters cast their ballot for Trump. And two polls after the midterm elections found that 76 and 79 percent of Jewish voters had voted Democratic.

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Matt Brooks, executive director of the Republican Jewish Coalition, said the group had been working for years to increase these numbers and that he saw some signs of success.

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He noted that Jewish support for Republican presidential contenders increased from about 10 to 15 percent during the two election cycles in the 1990s to 20 to 25 percent in the past 20 years. But those percentages are still on the low end of Jewish support for Republican candidates over the past century.

“We’re very confident that we’re going to continue to build on that and increase the share of the Jewish vote in 2020,” Brooks said in an interview. “We’re swimming upstream against 80 years of entrenched Jewish history voting Democratic. … We’ve always said it’s not going to be one election that defines us, but making incremental inroads to chip away at this long-standing link between the Jewish community and the Democratic Party.”

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Boxer said that Jewish support for Democrats was rooted in an identity as a minority group. He said he doubted that Trump — who has been accused of employing anti-Semitic imagery and symbolism as a candidate and who as president defended a group that had marched and chanted “Jews will not replace us” in Charlottesville — would end up attracting more Jewish voters during his reelection campaign.

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“Pretty much by definition, as far as Jews are concerned, there’s no such thing as a fine neo-Nazi,” Boxer said. “So if you’re siding with them you’re siding against us. It’s really black and white.”

Tensions have grown in the past week about the way Jewish concerns are being used for political ends.

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Jonathan Greenblatt, chief executive of the Anti-Defamation League, criticized Trump’s tweet Tuesday for this reason. “When #anti-Semitism is repeatedly politicized, it not only hurts the Jewish community, it fosters division,” he wrote on Twitter. “At a time when #anti-Semitism is rising, we need leaders to lead and fight #hate rather than point fingers and cast blame.”

A comic by liberal cartoonist Eli Valley that skewered Meghan McCain after she became emotional while sharing concerns about anti-Semitism and Omar on “The View” seemed to strike a nerve after going viral online. McCain, who is not Jewish, accused Valley, who is, of anti-Semitism.

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And it is not clear the “Jexodus” will materialize in the future. (A similar effort to woo black voters to the Republican Party is fighting a similarly uphill battle; 90 percent of black voters pulled the proverbial lever for Democrats during the 2018 midterms, according to Pew).

In an interview, Halie Soifer, executive director of the Jewish Democratic Council of America, cited polls that showed that only about 17 percent of Jews supported Republican candidates in the midterm elections.

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“This is not a coincidence,” she said, citing the Trump administration’s family separation policy, its travel ban that targeted predominantly Muslim countries and its work to dismantle the Affordable Care Act. “This is a rejection of Trump and his policies. His policies are antithetical to Jewish values."

Soifer said she didn’t take the Republican Party’s uproar about Omar at face value.

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“When President Trump invoked anti-Semitic tropes and conspiracy theories on his campaign, Republicans were silent. When President Trump equated white supremacists and neo-Nazis with those protesting them, Republicans were silent. And when leading Republicans, including Minority Leader McCarthy, invoked tropes, Republicans were silent,” Soifer said. “So this is the height of hypocrisy.”

Correction: A previous version of this article misspelled Halie Soifer’s name.