In a crucial swing state where the most important political races are often decided by the slimmest of margins, South Florida’s Jewish voters have become a key demographic in the battle for Florida governor.

A contentious campaign dominated by identity politics has been peppered with cries of anti-Semitism as GOP nominee Ron DeSantis highlights opponent Andrew Gillum’s ties to organizations critical of Israel. On Thursday, amid increasingly rancorous rhetoric, POLITICO reported that voters with Jewish surnames received text messages repeating comments that Gillum’s running mate, Chris King, made 20 years ago about being “nailed to the cross” by the mostly Jewish editorial board of Harvard’s student newspaper.

Gillum’s campaign quickly condemned the texts as “smear tactics.” A spokesman for DeSantis — who has dealt with allegations of racism and early in the campaign disavowed offensive robo-calls mocking Gillum by a neo-Nazi group — retorted that the Democratic nominee “should spend more time addressing why [King] said them and less time about how voters are finding out about them.”

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The back-and-forth is unlikely to be the last on the topic, because Florida’s Jewish vote, most of which is located below the northern boundary of Palm Beach County, could be crucial to the final decision on who becomes the state’s next governor.

Jewish Floridians — estimated at around 630,000, or 3.4 percent of the state’s population — are among the most reliable voting blocs in the state. There’s no solid estimate of Jewish voters in Florida, but the number would be around 470,000 if the community comprises 3.4 percent of the state’s voting population, notes Matthew Isbell, a Democratic consultant.

That’s a substantial number in a state where shifts in support can make a difference with tight top-of-ticket races. Jewish voters have historically voted Democrat at a roughly 70 percent clip, but boost that percentage — or depress it — and the election math changes.

Knowing this, DeSantis has attacked Gillum — who is ahead in the polls — all week over his relationship with groups like the Council on American-Islamic Relations and the Dream Defenders, which have supported a movement to punish Israel financially over its treatment of Palestinians. During a campaign stop in Miami, DeSantis didn’t answer a question about whether he believes Gillum is anti-Semitic, but pivoted into a criticism of the Dream Defenders.

The Dream Defenders “want to boycott, divest and sanction Israel, which I do think is an anti-Semitic movement because you’re taking the only Jewish state in the world, and you’re applying special sanctions on them,” said DeSantis, who attended the opening of the U.S. Embassy in Jerusalem this May. “That is unacceptable.”

Ira Sheskin, director of the Jewish Demography Project at the University of Miami, recently told the Miami Herald that his studies have found that issues of Israel typically rank low among the top issues for American Jewish voters.

“There are people out there who any mention of Jews in a negative light is going to raise some eyebrows on whether they want to vote for somebody like that. That’s particularly true in the 75-and-older population,” he said. “Anything that sounds like anti-Semitism could in fact cost the Democratic Party some votes.”

Sheskin, though, said “I don’t think it’s going to make that much of a difference.”

Sensitive to this, Gillum has been proactive in explaining that he opposes the Boycott, Divest and Sanctions movement, and that he supports the nation of Israel even if he opposed the moving of the embassy to Jerusalem. Meanwhile, Gillum’s supporters in the Jewish community have criticized DeSantis for what they say is divisive rhetoric.

“It is unfortunate that the DeSantis campaign is using hate and fear in an attempt to drive a wedge in the Jewish community,” said Alex Heckler, a Jewish lobbyist who had Gillum to his Miami Beach home recently to talk with Democrats about Israel and other campaign issues.

Evan Ross, a Jewish political consultant and Miami-area Democrat, added that he doesn’t think King’s comments, made in 1998 when he was running for student council president, will harm the Gillum campaign. King has said he regrets the remarks, which the Republican Governors Association highlighted as soon as Gillum picked the Winter Park businessman as his running mate.

But Sheskin’s research has shown that, even if Israel isn’t a driving issue for most Jewish voters, it’s more important among the minority of Jewish registered Republicans. And given that Florida Republicans have made the issue a talking point since late August, it’s unlikely that DeSantis will let up before November — and equally unlikely that Gillum will back down.

“Ron DeSantis is good on Israel,” Ross said, “and terrible on nearly everything else that matters to Floridians.”

Herald staff writer Jimena Tavel contributed to this report.