In the case of Specter, the five-term Republican-turned-Democratic senator, that has meant taking the rare step of rebuking President Obama -- over public criticism of Israel.
Both candidates spoke at a recent local event for the American Israel Public Affairs Committee and a candidates’ forum at the state’s largest synagogue, Reform Congregation Keneseth Israel, in the Philadelphia suburb of Elkins Park.
Sestak, who is now serving in the U.S. House of Representatives, also sought and recently received a closed-door meeting with officials of the Jewish Federation of Greater Philadelphia and other communal leaders.
At stake in the May 18 election is the career of one of the longest-serving Jewish members of the Senate.
Regardless of the outcome, Specter’s decision last year to leave the GOP and run for re-election as a Democrat left the Senate without a Jewish Republican. More specifically, it also marked the first time in decades that a moderate GOP Jewish voice -- embodied over the years not only by Specter but also Rudy Boschwitz of Minnesota, Warren Rudman of New Hampshire and the late Jacob Javits of New York -- was absent from the Senate.
Specter switched parties in the wake of his vote in favor of the federal stimulus package and poll numbers that showed he couldn't win another GOP primary. He instantly received endorsements from top local and national Democrats, including key Jewish figures in the party.
Even during his decades as a Republican, Specter received support from Jewish backers who typically reserved their donations and votes for Democrats. In large part that was due to his liberal positions on a host of domestic issues -- including abortion, church-state separation and civil liberties -- that often put him to the left of conservative Democrats from outside of Specter’s home turf of Philadelphia and the surrounding suburbs.
At the same time, Specter managed to command the support of the state’s Jewish Republicans and foreign policy hard-liners with his pro-Israel positions and support for stringent restrictions on U.S. funding for the Palestinian Authority.
And, of course, Specter always knew how to work a Jewish crowd.
Specter can likely count on the support of many of the Jewish community's movers and shakers, and he had his backers at Sunday's May 2 event at Keneseth Israel, attended largely by senior citizens.
Still, Sestak, a retired Navy admiral, has been working the Jewish community hard. Unwilling to cede any ground on that front, he has been reaching out to Jews publicly and behind the scenes throughout the campaign.
Polls of Democratic voters show Sestak gaining on Specter, with at least one survey showing the challenger with a slight lead.
When Specter switched parties last spring to run as a Democrat -- in part to avoid the GOP primary against challenger Pat Toomey -- he portrayed himself as a staunch ally of the president. And in an interview with the Jewish Exponent in November -- before the latest flare-up over settlements between the United States and Israel, but after tension between Jerusalem and Washington had been simmering over the issue -- Specter was reluctant to criticize Obama directly.
In a March speech on the Senate floor, he urged both Jerusalem and Washington to cool down their rhetoric, but refrained from outright criticism of the president.
In remarks at Keneseth Israel, however, Specter took direct aim at Obama. The senator told the crowd that the president's "heart is in the right place" on Israel, but that Obama needed more information and experience when it comes to the Middle East.
"I say publicly: You are wrong, Mr. President," Specter said, referring to the administration's call for Israel to cease building in eastern Jerusalem and news reports of Obama's private chastising of Israeli Prime Minister Benjamin Netanyahu.
"Jerusalem is where we Jews have built for thousands of years. It is different from the rest of the West Bank," he said to the crowd of 60 people.
About twice that number were on hand to listen to Sestak, who spoke prior to the incumbent. In contrast to their televised debate the night before, Specter and Sestak were not in the room at the same time.
Specter added that in the wake of diplomatic tension that arose when Israel announced building plans as Vice President Joe Biden was visiting, Israel's ambassador to the United States sought his advice almost immediately. Specter recalled that he cautioned the ambassador, Michael Oren, to avoid using the word "crisis" in describing U.S.-Israeli relations.
Oren confirmed the exchange, saying that Specter was one of the legislators he contacted to clarify Israel's position on Jerusalem.
"The senator's advice and insights were much appreciated," Oren told the Exponent.
Sestak used most of his appearance at Keneseth Israel to focus on domestic issues such as health care. But when asked about Israel, Sestak -- who has taken flak for, among other things, signing a congressional letter in January urging Israel to lift its
economic blockade of Gaza -- spoke about his meetings with Israeli security officials, including his efforts to help Israel gain access to an American-made combat ship.
He also offered his own assessment that could be considered an indirect criticism of the administration's approach, although his campaign spokesman said it was more about moving forward than criticizing the president.
"Israel will be less willing to take risks for peace if it doesn't feel the U.S. is 100 percent behind it," Sestak said. "I strongly believe that Israel is our vital ally, but I honestly do believe that we and Israel are both more secure when there is peace."