The pressure of a very tight presidential race whose outcome Ohio could well decide has been compounded by the Senate candidacy of a conservative Jewish Republican, Josh Mandel, who has divided loyalties among the 80,000 Jews of Greater Cleveland.

An advertisement in the Cleveland Jewish News this week, paid for by a group called Jews for Israel 2012, asked this question: “Are you willing to bet the life of the Jewish people on this president?” It questioned Barack Obama’s willingness to defend an Israel “threatened by nuclear annihilation.”

Automated calls pour into Jewish households from John Bolton, the hawkish former U.N. ambassador, in which he warns that a vote for Romney is needed to save Israel from an Iranian bomb and Islamist extremists.

Mandel, a 35-year-old ex-Marine who has raised more than $20 million through conservative backers, has appalled Ohio’s socially progressive Jews — who are still the clear majority — with an anti-abortion stance that has included calling the Indiana Senate nominee Richard Mourdock a “class act” after Mourdock said pregnancy resulting from rape was “something that God intended to happen” and life was always “a gift from God.”

Oy vey. Does all this matter? Yes it does. It is that close in the Buckeye State. Ohio, with its 18 electoral votes, is abouttied, according to most polls. No Republican has won the White House without carrying Ohio. This is the swing state most likely to swing things. Conservative-backed billboardsscreaming “Voter fraud is a felony” have prompted the countermessage that, “Voting is a right, not a crime.” Republican intimidation meets Democratic determination.

Obama needs to win big in Cuyahoga County, which includes the strongly Democratic inner city of Cleveland, to carry the state. That is what he did in 2008, gaining 68.5 percent of the vote and winning by a margin of nearly 250,000 votes — enough to secure victory by just over 200,000 votes in Ohio. The Romney campaign reckons that if it can cut Obama’s margin in Cuyahoga to about 175,000 it will take the state.

About 80 percent of Cleveland’s Jews are believed to have voted for Obama last time. Robert Goldberg, former chairman of the United Jewish Communities (now The Jewish Federations of North America) and a Romney supporter, said he believed that number would drop to 60 percent this time. “Jews just don’t trust Obama on Israel,” he told me. “The president has no sympathy for Israel. His sympathy is for the Muslim world he knew as a child.”

If Goldberg is right about a shift, that would be significant. He argues that Obama is anti-business and anti-Israel and believes a faltering economy above all is pushing Jewish voters to change position. (Polls in Israel show Israelis strongly favoring a Romney victory.)

The case I heard in Ohio against Obama on Israel was the usual Republican hodgepodge of insinuations: The president went to Cairo but not Jerusalem, he snubbed Prime Minister Benjamin Netanyahu, he reached out to Muslims but showed no love for Jews. They ignore all the defense and intelligence cooperation that led the Israeli defense minister, Ehud Barak, to say Obama had done “more than anything that I can remember in the past” for Israeli security.

Mandel has also been playing the Israel card in pursuit of the Jewish vote, despite the fact his opponent, the Democrat incumbent Sherrod Brown, co-sponsored the United States-Israel Enhanced Security Cooperation Act of 2012, legislation that deepens defense cooperation.

Among those troubled by Mandel’s campaign is Austin Ratner, a novelist and the son of James Ratner. Mandel is related by marriage to the Ratner family. Austin Ratner wrote apiece this month in the Jewish Daily Forward arguing that family and tribal Jewish loyalty were misplaced in the political sphere, where reason must prevail.

He quoted his aunt, Deborah Ratner, a major Democratic fund-raiser, telling Mandel at a family gathering: “I don’t want this to be awkward, but you represent everything I’ve spent my life working against.” He also said some Democrat relatives “have supported Mandel’s campaign out of family loyalty” — a form of loyalty, he suggested, that “leads deeper into the darkness.”

The Jews of Cleveland are arguing at high volume. They are good at disputation. In this case the argument could change the course of things far beyond Cleveland.

James Ratner sent me an e-mail saying, “This may well be a case where the noise is obscuring the music.” Beneath all the shouting, he suggested, Jewish sentiment remains solidly Democratic. “In a meeting this week of 60 members of a woman’s group at Park Synagogue there was absolute unanimity behind Obama. No one was voting for Romney.”

Those Jewish women know exactly what Romney and Mandel represent: an obscurantist and invasive threat to their rights in the name of a God whose wishes these men presume to know.