Few issues in American politics are as bipartisan as support for Israel. Yet the question of whether President Obama is supportive enough is behind some of the most partisan maneuvering since the Middle East ally was born six decades ago, and that angling has potential ramifications for the 2012 elections.

The visit of Prime Minister Benjamin Netanyahu of Israel in the past week captured just how aggressively Republicans are stoking doubts about Mr. Obama. Republican Congressional leaders and presidential aspirants lavished praise on Mr. Netanyahu as quickly as they had condemned Mr. Obama for proposing that Israel’s 1967 borders, with mutually agreed land swaps, should be a basis for negotiating peace with the Palestinians.

Republicans do not suggest that they can soon break the Democratic Party’s long hold on the loyalty of Jewish-American voters; Mr. Obama got nearly 8 of 10 such voters in 2008. But what Republicans do see is the potential in 2012 to diminish the millions of dollars, volunteer activism and ultimately the votes that Mr. Obama and his party typically get from American Jews — support that is disproportionate to their numbers.

While Jewish Americans are just 2 percent of the electorate nationally, they are “strategically concentrated,” as Mark Mellman, a Democratic pollster, put it, in several swing states that are critical in presidential elections. Those states include Florida — which in 2000 illustrated the potentially decisive power of one state — Ohio and Nevada.

A test of Mr. Obama’s support will come June 20, when he will hold a fund-raiser for about 80 Jewish donors at a private dinner.

John R. Bolton, the former United States ambassador to the United Nations and a possible Republican presidential candidate, argues that because of administration proposals, Republicans will be able to make gains not only among American Jews but also among evangelicals who are supportive of Israel on biblical grounds, and other voters.

Mr. Bolton said that he was on a cruise sponsored by the conservative magazine Weekly Standard last week in the Mediterranean, and that most of the people on the ship “reacted very strongly against” Mr. Obama’s speech outlining his Mideast vision. “As a Republican,” he said, “you can use this to show how radical the president’s policies are on a whole range of issues.”

The depth of Democrats’ worries was evident from the competition to out-applaud Republicans on Tuesday during Mr. Netanyahu’s speech to a joint meeting of Congress and from the speed with which Congressional Democrats led by Senator Harry Reid of Nevada, the majority leader, distanced themselves from Mr. Obama on Israel.

“Are there questions in the American-Jewish community? I think the answer is yes,” said Mr. Mellman, who is Jewish and has polled the community for Democrats in the past. “Has Obama been branded as not pro-Israel or anti-Israel? Not at all.”

“I think he is strongly pro-Israel, in fact,” he added. “But that is the political struggle in which the Republicans are engaged, which is to get him branded as not pro-Israel. And to the extent they’re successful in that, the likelihood is they would have some meaningful impact on the Jewish vote.”

J Street, the left-leaning alternative to the more established American Israel Public Affairs Committee, put out a statement of support for Mr. Obama on Wednesday. “To oppose the president without laying out a credible alternative basis for a two-state solution is to embrace a status quo leading to the eventual loss of Israel as we know and love it,” its statement said.

Mr. Obama’s proposal, the group said, is supported by many Jews in the United States and Israel. It is “the path that most of Israel’s recent prime ministers have attempted to blaze, from Rabin to Barak to Olmert.”

Republicans, however, are confident that their emphasis on unconditional support for Israel holds appeal both for many Jews and for conservative Christians.

Yet it is the Republican Party’s close identification with evangelical Christians in recent years that is perhaps its biggest hurdle to winning over significant numbers of Jewish voters and donors. On issues that are crucial to the conservative Republican base — like opposition to abortion, gay rights, liberalized immigration and much government spending — most American Jews are on the other side, and strongly so.

“If Republicans can mischaracterize this president as anti-Israel, they can distract from the fact that on every other issue their party is in disagreement with the American-Jewish community,” said David A. Harris, president of the National Jewish Democratic Council, a group of Jewish-American Democratic activists.

Mr. Netanyahu on Monday experienced first-hand the tension arising from that complaint among Democrats, and Republicans’ rejection of it, in a private meeting he held with representatives of the National Jewish Democratic Council and the Republican Jewish Coalition to underscore American Jews’ bipartisan consensus on Israel.

A partisan argument ensued after Representative Debbie Wasserman Schultz of Florida, whom Mr. Obama recently named as chairman of the Democratic Party, suggested they agree not to make support for Israel an election issue. Matt Brooks, executive director of the Republican group, objected, accusing her of proposing a “gag order.”