NEW YORK — For the past four years, Jewish conservatives have been working hard to paint President Obama as too willing to press Israel on Palestinian issues. 

But the latest Washington buzz could throw a wrench in that line of attack — if, as some Washington insiders are suggesting and the Drudge Report is reporting, Mitt Romney chooses Condoleezza Rice as his running mate.

That’s because as secretary of state during the George W. Bush administration, Rice was a strong backer of Palestinian Authority President Mahmoud Abbas, whom she described as a true partner for peace. She pushed hard for Palestinian elections, which in 2006 resulted in a victory for Hamas (in a 2008 essay in Foreign Policy magazine she held firm to the notion that elections were the right way to go despite the outcome). She described the Israeli-Palestinian conflict as vital to solving the Iran problem, and she was the administration’s point person for pursuing Israeli-Palestinian negotiations, forging close ties with Israeli leaders who favored negotiating with the Palestinians. In 2007 at the summit meeting in Annapolis, Md., she reportedly told a closed-door meeting of Israeli and Arab envoys that her childhood experience with segregation in the South helped her understand the Palestinian experience.

“Questions will be raised on where she stands on Israel,” said Jonathan Tobin, senior online editor at Commentary magazine. “I think it would make it a little harder for Jewish Republicans to use the issue of support for Israel against the Democrats.”

Morton Klein, the national president of the Zionist Organization of America and a frequent critic of the Obama administration, sounded a similar note.

“It understandably would be concerning to us if he’s picking somebody who shows herself to be hostile to Israel and to U.S.-Israel relations,” said Klein, who often criticized Rice when she was secretary of state. “She pressed Israel to make one-sided concessions while not making sure the Palestinians fulfilled their obligations.”

The speculation over Rice comes as Romney prepares to visit Israel later this month. So far during the campaign, the bulk of Romney’s attacks on Obama have focused on domestic issues related to the economy. But one area where the presumptive Republican nominee has sought to draw a foreign policy distinction is on Israel, accusing the president of being too willing to side with the Palestinians and not always standing strong with the government of Prime Minister Benjamin Netanyahu. By contrast, Rice’s criticism of Obama on the handling of Israeli-Palestinian issues has been more tactical — for example, in an interview with Foreign Policy magazine, she argued that pushing for an Israeli settlement freeze was a mistake because it put Abbas in the position of having to be even more demanding by comparison.

At the same time, some analysts note, a close look at Romney’s positions and Rice’s show little differences of policy when it comes to Israel. Both declare themselves champions of Israel’s right to defend itself. Both support the two-state solution (though Romney has steered clear of emphasizing that point during most of the campaign).

But where Romney has no history in foreign policy for hawkish pro-Israel critics to seize upon, Rice does. And while candidate Romney can stake out Israel-friendly positions like promising to make Israel the site of his first overseas trip as president, Rice has what many Jewish conservatives would see as baggage.

On the wider, overall topic of foreign policy, Rice has drawn conservative plaudits in recent weeks as she’s echoed Romney in painting Obama as an ineffectual leader who has failed to lead on the world stage.

In any case, any speculation about how Rice could affect the Jewish vote is a bit premature – or, some say, far-fetched.

“Politicians of all stripes have always used the menu of V.P. selection as a way to court different constituencies,” said David Makovsky, a senior fellow at the Washington Institute for Near East Policy. “With polls showing that Romney faces a deficit when it comes to women voters, it is not surprising that his campaign would raise this possibility at this time. However, the actual selection may be based on a different set of criteria, and foreign policy experience may be only one variable in this decision.”

On the one hand, Rice could make an attractive No. 2 for Romney. She’s got plenty of foreign policy experience, and she’d have some appeal to at least two key voter demographics: women and African Americans. She could also help sway undecided voters.

Yet while independent voters might welcome Rice on the ticket, conservatives likely would not. Her pro-choice stance is a non-starter for many Republicans, and in many foreign policy debates during the George W. Bush years, Rice played the relative dove to Vice President Dick Cheney’s hawk – especially when it came to the Middle East and especially in the second term after she had shifted from being national security adviser to secretary of state.

It seems unlikely that Romney, whose Mormon background and non-ideological past as Massachusetts governor already have stoked misgivings among conservative Christians, would go with someone who doesn’t appeal to the Republican Party’s conservative base.

“The notion that Romney would choose someone who doesn’t have a pro-life position on abortion seems to me entirely a fantasy that makes no sense for him,” Tobin said.

But what if Romney did choose Rice? Would that cut into conservative support for Romney?

“She’s been much harder on Israel than he professes to be, and whether that would satisfy his core base of conservative and evangelical adherents is an open question,” said Seymour Reich, a former chairman of the Conference of Presidents of Major American Jewish Organizations.

When Bush was president, Rice often invited Reich to meetings with Jewish communal leaders when she sought a more dovish voice to counter those further to the right.

As with any president running for a second term, this election is, perhaps more than anything else, a referendum on the incumbent. By that count, the person that occupies the bottom half of the Republican ticket is really a side issue.

“For Jews I don’t think it will have an impact because as president Romney is the one who makes the decisions,” Reich said. “Those who are unhappy with Obama on Israel will not let Rice deter them from supporting Romney. It’s the top of the ticket that always counts.”