President Trump’s demand this week that Jewish voters abandon the Democratic Party isn’t working out so well.

If anything, it has made George Arthur, 72, a Jewish voter in the Philadelphia suburbs “more inclined” to stick with Democrats next year. His wife was even more adamant that Mr. Trump’s overtures are falling flat.

“I love Israel. There are some issues there. But I find it very insulting that he would question the loyalty of very loyal Jewish-American Democrats,” she said. “Looking at Trump … I don’t know if I have enough adjectives. He is crude. He’s pompous. He’s arrogant. He’s narcissistic.”

Their reactions reflect the stark polarization of American politics today, with Jewish voters who historically align with the Democratic Party unlikely to switch even when offended by anti-Israel rhetoric from Democratic lawmakers such as Reps. Rashida Tlaib of Michigan and Ilhan Omar of Minnesota.

Mr. Trump has repeatedly used as a wedge issue the Israel-bashing comments, including anti-Semitic tropes, by Ms. Tlaib and Ms. Omar, who last year became the first Muslim women to serve in Congress.

He upped the ante Tuesday by saying Jewish Americans who vote for a Democratic Party that has embraced the two women showed “either a total lack of knowledge or great disloyalty.”

The comments came under fire for being an anti-Semitic trope about Jews having divided loyalties, the same trope for which Ms. Omar refused to apologize in March for using.

Mr. Trump doubled down Wednesday, insisting his words were not anti-Semitic while repeating the warning to Jewish voters.

“If you vote for a Democrat, you’re being disloyal to Jewish people and you’re being very disloyal to Israel,” he told reporters at the White House.

His brickbat at Democrats followed Israel’s barring of a visit last week by Ms. Omar and Ms. Tlaib. Israel then permitted Ms. Tlaib, who is the U.S.-born child of Palestinian immigrants, to visit under a gag order, but she refused.

Ms. Omar responded by suggesting the U.S. cut aid to Israel.

Mr. Trump, whose daughter Ivanka converted to Judaism after marrying Jared Kushner and is raising their children in the Jewish faith, has made strong support of Israel a mainstay of his foreign policy.

Senate Minority Leader Charles E. Schumer, New York Democrat, accused Mr. Trump of stirring up anti-Semitism around the world.

“To my fellow American Jews, particularly those who support President Trump: When President Trump uses a trope that has been used against the Jewish people for centuries with dire consequences, he is encouraging — wittingly or unwittingly — anti-Semites throughout the country and the world. Enough,” he said in a statement.

The 2020 Democratic presidential candidates also took offense.

“I am a proud Jewish person, and I have no concerns about voting Democrat,” said Sen. Bernard Sanders of Vermont, jesting that he even plans to give America its first Jewish president in 2021.

Former Vice President Joseph R. Biden called the comments “insulting and inexcusable.”

“Stop dividing Americans and disparaging your fellow citizens. It may not be beneath you, but it is beneath the office you hold,” he tweeted after Mr. Trump’s first remarks about “disloyalty.”

As an electoral strategy, Mr. Trump’s pleas target a relatively small group of voters who overwhelmingly back Democrats in presidential elections.

About 74% of Jewish voters identify as Democrats or lean toward the Democratic Party, compared with 24% who identify as Republicans or lean GOP, according to a 2016 study by the Pew Research Center.

Yet a small move in the Jewish vote could make a big difference in a close election in swing states next year.

Mr. Trump carried the must-win state of Florida by a 1.2 percentage point margin in 2016. Exit polls showed Jewish voters accounted for 4% of the turnout in the Sunshine State.

In Pennsylvania, Mr. Trump won by less than a 1 percentage point margin, putting him over the top in electoral votes needed to win the White House. About 2.3% of the Pennsylvania population is Jewish, according to the 2018 American Jewish Year Book. Exit poll data for the Jewish vote in 2016 in Pennsylvania was not available.

Nationally, Mr. Trump’s 24% of the Jewish vote in 2016 was the smallest share that a Republican presidential candidate had received since George W. Bush garnered 19% in 2000.

Hillary Clinton received 71% of the Jewish vote in 2016, and the rest went to Libertarian and Green party candidates in the largest third-party vote by Jewish Americans in recent years. Mr. Trump potentially can make inroads with that group.

Marc J. Hetherington, a scholar of voter behavior at the University of North Carolina, said Mr. Trump’s appeal is more likely aimed at shoring up existing support among conservative Jewish voters.

“In this polarized political environment, it is unlikely that voters of any faith or background will change their party alignments very much,” he said. “Among Jewish voters, those who are more Orthodox already tend to favor Republicans, and it is that group which President Trump seems to be appealing to with his recent actions.”

Howie Beigelman, executive director of Ohio Jewish Communities, said he witnessed “strong pushback” against Ms. Omar and Ms. Tlaib, but it didn’t persuade Jewish voters to quit the Democratic Party.

He said courting Jewish voters isn’t new for Republicans, though Mr. Trump has put a new spin on it.

“Every four years there is an attempt to change it,” he said. “People hardened in their positions. … I haven’t seen any kind of movement in either party.”

The Democratic Party, which for the first several decades of the U.S.-Israeli alliance was the more pro-Israel party and the home of most Jewish voters, has contended in more recent years with demographic changes in its coalition and an increasing number of far-left activists who support such groups as the Boycott, Divestment, Sanctions (BDS) movement against the Jewish state.

Still, Mr. Trump’s comments sparked a fierce backlash from Jewish groups.

The Simon Wiesenthal Center, a Jewish human rights group that fights anti-Semitism, vouched for America’s longtime bipartisan support for the Jewish state.

“To say otherwise, and depend only on one party — particularly in these turbulent times of increased hate and anti-Semitism — weakens and divides the most important Jewish community in the Diaspora,” Rabbi Marvin Hier, the center’s founder and dean, and Rabbi Abraham Cooper, the center’s director of global social action, said in a joint statement.

Aaron Keyak, former head of the National Jewish Democratic Council, accused Mr. Trump of inadvertently inciting violence against Jews.

“We have seen throughout history how dangerous it is when our rulers accuse us of disloyalty. We’re begging the president and those around him to make this stop,” Mr. Keyak said. “I know the president doesn’t want any violence against us, but he has to stop before somebody takes up the cause and acts against us ‘disloyal’ Americans.”

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