Moments after Mitt Romney completed his ode to Israel in front of Jerusalem’s old stone walls on Sunday, reporters asked Sheldon Adelson, the casino mogul and a financial rabbi for the presidential campaign, whether the speech would convince Jewish voters back home to vote for the Republican.

“If they hear it,” answered Adelson, who was with Romney in Israel and has pledged tens of millions of dollars to pro-Romney super PACs. “Yes, for sure.”

“I heard it!” said Margie Rosen, 84, leaning on her cane outside Sage Bagel and Deli on Monday morning. A clock above the selection of white fish and black-and-white cookies read, “Be a Mensch. . . .” Rosen agreed with Romney that Jerusalem should be the capital of Israel, but she didn’t like that he talked about it publicly. “That’s a problem they have to solve.”

Other members of Romney’s intended audience of elderly Jewish voters in this condo-dotted coastal town between Miami and Fort Lauderdale also were unswayed.

“I listen to some of these Jews in here saying Obama is not a friend of Israel,” said Mark Axelowitz, 64, as he walked into the bagel place, “and I say, ‘think of Social Security and Medicare!’ ”

Scott Margules, 55, who walked out with an order of sable, criticized the Republican presidential hopeful for trying to “pander to the Jewish vote” in this swing state.

Every four years, American politics enters a mystical period. Elected officials, campaign operatives and the news media wonder whether this election might be different from all the others. Republicans saw an opening in 2008, when Barack Obama was depicted by some of his more animated critics as the crypto-Muslim personification of “bad for the Jews.” But the Democratic candidate won 75 percent of the Jewish vote.

Could 2012 be the year? Today, Obama’s numbers among Jews have dipped into the 60s, according to recent polls, and Republicans are hoping the drop has less to do with a lousy economy than with Obama’s early, aggressive efforts to move the Mideast peace process along with sometimes blunt criticism of the Israeli government. They are hoping for a conversion among lifelong Democrats, an influx of donors and reassaurance for evangelicals, for whom the protection of the Holy Land is a top issue.

Measure of friendship

In February 2008, Obama told Jewish voters in Cleveland, “There is a strain within the pro-Israel community that says unless you adopt an unwavering pro-Likud approach to Israel, then you’re anti-Israel, and that can’t be the measure of our friendship with Israel.” His appointment of Sen. Hillary Rodham Clinton of New York — a supporter of Israel — as secretary of state gave him some cover, but Clinton astonished many when, in May 2009, she said the administration “wants to see a stop to settlements — not some settlements, not outposts, not natural-growth exceptions,” a sentiment Obama echoed in a subsequent speech.

Some of the staunchest Democratic supporters of Israel were willing to cut the president some slack in hopes of nudging the peace process forward. It didn’t move, and the relationship between Obama and Israeli Prime Minister Benjamin Netanyahu grew more strained. Jewish supporters of Obama — worried that the president had gone too far in pressuring Israel — closed down the space for debate. Although Obama has publicly and strongly reiterated U.S. support for Israel, Jewish Democratic lawmakers now find themselves having to beat back concerns among some that Obama would return to the previous strategy if elected to a second term.

The numbers don’t provide much hope for Republicans: Only about 6 percent of American Jews vote solely based on Israel-centric issues and most of them are already reliably Republican.

“This is a four-year ritual that the Republicans go through,” said Rep. Debbie Wasserman Schultz, the first Jewish congresswoman from Florida and chairwoman of the Democratic National Committee. “Jews categorically disagree with everything in the Republican Party’s agenda domestically,” she said, and Romney has sought to peel off some support in battleground states like Florida by sowing doubt about Obama’s commitment to Israel.

Still, she finds herself trying to gloss over some of president’s earlier actions. “I wouldn’t focus so much on one particular comment here or there throughout what is such a close relationship,” Schultz said during a pause from a seniors’ event in an Aventura condominium. She pointed to U.S. military aid to Israel and argued that the president’s record was identical to Romney’s bluster. “You can’t put a magnifying glass up close on every single utterance of the president of the United States and dissect it for meaning that isn’t there,” she said.

That, of course, is exactly what Romney hopes to do.

“Standing by Israel does not mean with military and intelligence cooperation alone,” Romney said in Israel. “We cannot stand silent as those who seek to undermine Israel voice their criticisms. And we certainly should not join in that criticism. Diplomatic distance in public between our nations emboldens Israel’s adversaries.”

Playing to the audience

Romney’s chiding of the president went over big among his donors in Jerusalem. On Monday morning, he raised about $1 million at the King David Hotel with Adelson seated to his left. Across the seas in Miami, the Republican Jewish Coalition, a $6.5 million anti-Obama campaign funded in part by Adelson, met Monday evening.

During their gathering at Too Jay’s deli in Plantation, members of the group discussed how to nab the Jewish vote and beat Obama. Three men in sports blazers lectured about a dozen people that their polling was so good that they “could tell you whether you preferred tennis or golf.” Even so, one woman expressed some skepticism that the group could dent the Democratic block. “They are strictly Democrats and they are not changing!” said the woman, who declined to give her name. “How are you going to change their minds? They just say, ‘oy vey.’ ”

But even the most motivated of Jewish voters against Obama are less concerned with the state of Israel than the state of America. Nat Trayger, 60, a medical salesman from Broward County who attended the meeting at Too Jay’s, was optimistic about Romney winning Florida’s Jewish vote. “Because Jews, as Americans, are unhappy with the way things are going,” he said.