WASHINGTON — With every new swipe at President Barack Obama’s exotic background or cultural influences, a contingent of Republican leaders are signaling that they believe the coming elections are more than just a referendum on the administration’s economic policies. Rather, to a degree that is striking, conservatives are also trying to make the fall campaign about the president himself and the kind of societal change he actually represents.

To understand why, one need only look to the Republican Senate primary in Delaware, where Christine O’Donnell this week became the latest in a series of conservative insurgents to jolt the party establishment. Such divisive primaries have threatened to reopen longstanding rifts within the party. And the increased focus on Obama’s personal history is probably less about persuading the electorate as a whole than it is about unifying the disparate strands of the conservative base.

The latest controversy over Obama’s identity involves — once again — Newt Gingrich, the former House speaker, who this week described Obama, whose father was a Kenyan economist and spoke out against the occupying force in his country, as exhibiting “Kenyan, anti-colonial behavior.” Gingrich was shorthanding an essay in Forbes by conservative theorist Dinesh D’Souza, who, in exploring Obama’s attitudes toward business, settled on the theory that Obama was taking directions from the anti-corporate apparition of his long-departed father. (That Obama never really knew his father is apparently beside the point.)

This latest uproar came about a month after prominent Republicans excoriated Obama for supporting the building of a community center and mosque near ground zero and just a few weeks after Glenn Beck, the television personality, held his faith-based rally on the National Mall. Last week, meanwhile, Gov. Haley Barbour of Mississippi, chairman of the Republican Governors Association, in tepidly acknowledging Obama’s Christian faith, said to reporters: “This is a president we know less about than any other president in American history.”

This cultural critique of Obama — a general portrayal of otherness based on his age and ideology, his upbringing and, inescapably, his race — is reminiscent of similar attacks on Bill Clinton, whom 1990s-era conservatives reveled in depicting as a symbol of the socially permissive, self-indulgent hippie left. To this point, these attacks seem to be having little influence on the general electorate. In June, according to Andrew Kohut, director of the Pew Research Center poll, only about 28 percent of voters said their vote in November would be a vote against Obama, and Kohut said soon-to-be released data would show little change.

David Winston, a Republican pollster, summed up the average voter’s response to the Republican attacks this way: “The mosque is an interesting point, but tell me how you’re going to get jobs and fix the economy.”

What’s important for Republicans, though, isn’t necessarily the viability of this assault with a broad swath of the electorate but rather that it seems to resonate with Republican constituencies who haven’t always been able to find common cause and whose turnout in November could be crucial.

Since the 1960s, the modern conservative movement has been an amalgam of three distinct factions: the champions of free enterprise, the foreign policy types often described as neoconservatives, and the social conservatives who became the spine of the party’s grass-roots campaign apparatus.

It was a fear of communism that nicely unified all of these groups in the Cold War years. The Soviet Union and its satellites were Marxist in their economic outlook, expansionist in their foreign policy and defiantly godless in their culture. Stan Lee could not have dreamed up a more perfect nemesis around which Republicans could coalesce.

For most of the past 20 years, however, Republicans have struggled to keep these groups equally engaged. George W. Bush juggled an agenda of interventionist military policy, tax cuts and opposition to stem cell research and gay marriage — in other words, something for everyone in the fold. But then the war in Iraq and soaring deficits splintered the conservative coalition and led, ultimately, to a Democratic takeover.

If Ronald Reagan was the party’s Great Communicator, then Republicans seem to be hoping that Obama is its Great Galvanizer. The assault on Obama’s cultural affinity, the clear implication that he is neither suitably Christian nor American in his values, adds a sinister subtext to the argument against his economic agenda. It suggests that Obama is oddly indifferent to the effects of his policies on ordinary Americans because, at the end of the day, he doesn’t share their experience.

Obama’s alleged sympathy for so-called Muslim extremists who would desecrate the World Trade Center site, his socialist African ancestry and his early years in Indonesia — all of this creates a shadowy archetype that every conservative enclave, fiscal, foreign policy and religious, can find a reason to fear.

You can probably expect the tenor of these attacks to grow shriller as 2012 approaches and Republican presidential hopefuls begin courting activists in Iowa. For now, at least, the president has no plans to respond — perhaps other than to affirm his Christianity more regularly than he used to. White House advisers contend that as the conservative insinuations about Obama grow more pronounced, the extremism that underlies them will become self-evident to the public.

In the meantime, though, the November elections are less than seven weeks away. And by energizing the grass roots, the constant innuendo about Obama’s allegiances may be doing exactly what Republicans need it to do.