RICHMOND, Va. — The man looks incredulous, his voice rising in exasperation as he tells President Obama to stop demonizing small-business owners. “We need somebody who believes in America,” he says, right before viewers hear, “I’m Mitt Romney, and I approved this message.”


Minutes earlier on the same local NBC station here, anyone watching commercials between rounds of “American Ninja Challenge” would have seen Mr. Obama’s latest attack. As Mr. Romney sings a monotone rendition of “America the Beautiful” at a campaign rally, headlines flash on the screen describing how he put his fortune in foreign bank accounts and shipped jobs to China and Mexico.


As the presidential campaign has become a clash over a host of issues — from tax cuts to foreign diplomacy to claims of words taken out of context — Mr. Romney, Mr. Obama and their allies have started trading accusations over a much more delicate and personal question: Are you an American like me?


Their choice of words and imagery is a reminder of how powerful undercurrents of identity, wealth, race and religion are shaping this election. These surface in subtle and not-so-subtle ways as two candidates who can have trouble connecting with voters on a personal level try to define each other as detached from mainstream American life.


By Mr. Romney’s telling, the president has a “strange” and “foreign” political philosophy.


Mr. Obama has suggested that Mr. Romney’s vision of the American dream involves Indian call centers and Caribbean tax havens. “What is Mitt Romney hiding?” asks one recent ad.


For two men with unconventional biographies — one is the son of a Kenyan immigrant and the other a descendant of Mormon pioneers — this is risky but potentially fertile territory.


“It’s the ‘Mars attacks’ approach,” said Ken Goldstein, president of Kantar Media’s Campaign Media Analysis Group. “And it often works because nothing brings the people of Earth together like an invasion from Mars.”


Using attack ads in heavy rotation across battleground states like Virginia, along with carefully worded campaign speeches and barbed sound bites on cable television, Mr. Obama, Mr. Romney and their supporters are pushing these competing story lines as polls show negative views of both men are on the rise.


Neither candidate is accusing the other of sending subliminal signals over race or religion. And the language on the campaign trail is a far cry from the overt efforts to make religion a wedge issue — like the campaign by Representative Michele Bachmann and other Republican members of Congress to ferret out what they say is an Islamic extremist influence in government.


Rather, the Obama and Romney campaigns seem conscious of the dangers of going too far.


“These two campaigns have gone to pretty considerable lengths to keep away from that kind of attack that relates either to Obama’s race or Romney’s religion,” said Dan Schnur, director of the Jesse M. Unruh Institute of Politics at the University of Southern California and a former Republican consultant. “What we’re seeing is more like, He’s really rich so he can’t understand what your life is like,” Mr. Schnur said of attacks on Mr. Romney.


Against Mr. Obama, he added, the tack is, “He’s never had a real job, so he can’t understand how you built your business.”


Attack strategies against Mr. Obama have always been tricky to execute, not just because of possible racial tripwires but because a solid majority of voters say they like the president personally, whatever they may think of his politics.


The approach Mr. Romney has taken in recent weeks with increasing zeal seeks to avoid those sensitivities while planting doubts in voters’ minds about Mr. Obama’s fealty to America and its allies. Just this week, he accused the president of betraying “the national interest” by leaking national security secrets, and said in a CNBC interview that the president’s ideology is “very strange and in some respects foreign to the American experience type of philosophy.”


He was referring to the president’s recent statement that government investment has helped small businesses thrive, a comment that conservatives have pounced on as evidence that Mr. Obama is sympathetic to European-style social democracy