In York, Pa., he speaks of his father living at the local YMCA. In front of Toledo autoworkers, he calls himself the “son of an automobile man.” In Media, Pa., he is the “grandson of Ambrose Finnegan,” a Scranton ad man turned gas company worker. But he is also the great-grandson, on his mother’s side, of Edward F. Blewitt, a member of the Pennsylvania state Senate. On his paternal side, he is connected to Maryland through a great-great grandfather who sold produce and a grandfather whose transition from Baltimore kerosene salesman to Wilmington oil executive earned the family a temporary taste of wealth. His family was rich in Boston, comfortable in Long Island and broke in Scranton. One relative died in World War II, and another, “Old Man Sheen,” ran shipyards in Virginia.

Vice President Biden, the Obama administration’s traveling everyman, seems to have roots all over. He learned about some of his ancestral connections from stories told at the family dining table, but many details came to him from an unlikely source — a genealogist who burrowed into the cabinets of microfiche and stacks of bound registries at the Mormon church’s vast Family History Library in Salt Lake City.

“He called me out of the blue to see if I could do his genealogy,” said James W. Petty, a former senior researcher at the library. On a recent afternoon, Petty, wearing a tweed coat and a “certified genealogist” lapel pin, leaned back from the documents spread across a desk overlooking Temple Square. He recalled an initial 2004 conversation with the then-senator inquiring how his ancestors came to the coal mines of Pennsylvania’s Lackawanna County and put food on the table.

“I said, part joking, part serious, ‘It’s good for a politician because you can build on this culture, and this culture, and this culture. You can become a favorite son in three or more cultures.’ And he said, ‘I want to approach more people.’ He understood that all of this would affect how he connected with people.”

“He has a great interest in it,” Valerie Biden Owens said of her brother. “Your family gives you, hopefully, roots and wings.”

On Thursday, Biden put all his connections to full use in his debut role as the Obama reelection campaign’s relater in chief. He traveled to Toledo, where he called out Mitt Romney, Rick Santorum and Newt Gingrich by name as being “dead wrong” in their opposition to the autobailout.

“If you give any one of these guys the keys to the White House,” Biden said. “They will bankrupt the middle class again.”

It is a role that the gregarious, relationship-cultivating old pol seems to have been born to play, and one that has already helped his less-experienced and more distant boss negotiate the political ways and means of the capital. A four-decade creature of Washington, Biden works lawmakers, schmoozes donors, levels with conservatives and assures liberal groups. He has emerged as a top administration emissary to troublesome nations and a not-so-private inner-circle dissenter on issues such as health care, Afghanistan and a policy requiring employers to fund contraceptive coverage. Less willingly, he has brought comic relief at times as the nation’s goofy uncle and has provided a soap opera subplot to the no-drama Obama ethos, thanks to the Washington job-swap meshugas in which he and Hillary Clinton switch places.

On the campaign trail, there is an expectation that Biden’s empathetic style will stand out in a year when a struggling economy is the dominant issue, and candidates in both parties seem determined, whatever their acting skills, to try on the grits-eating, regular Joe persona. Four years ago, Biden served as the ambassador to white working-class enclaves that were deeply skeptical about Obama. This time around, he will travel more broadly with the intention of reaching people that the president has been unable to. His role, as advisers view it, is not only to testify to Obama’s steely nerves but also to be the more down-to-earth half of the ticket — the salty Middle-Class guy on the block who tells bad jokes, has real-life scars and convinces you that things are going to get better.

“Biden is someone we can send everywhere,” said Obama adviser David Axelrod, who noted that the president was “less revealing” than Biden. “Republicans are increasingly grinding and negative, and I think that contrast is beginning to bite now and it’s going to grow. Biden is a guy who can draw that contrast very well.”

* * *

The notion of Biden as master campaigner has some complications. His presidential runs have failed badly. Accusations of plagiarism led him to drop out of the 1988 presidential race. And in 2008, the week he officially announced his second bid for office, he ran into trouble by calling Obama “the first mainstream African American who is articulate and bright and clean and a nice-looking guy.” He withdrew after finishing fifth in the Iowa caucuses. His strong debate performances and long résumépersuaded Obama to take him to the White House, but as vice president, he also brought along a reputation for loose talk.

Typing the word “Biden” into Google prompts the search engine to suggest “Biden gaffes.” The Photoshopped image under the Onion headline “Shirtless Biden Washes Trans Am In White House Driveway” has led to viral Web versions of “Uncle Joe,” depicting Biden, who does not drink, as a genial, cringe-inducing drunk. A slideshow on the Web site Buzzfeed titled “Pictures that Show What Joe Biden is Really Like” features thought bubbles of him in Oval Office meetings pining for hot dogs and singing the praises of the sitcom “Two and a Half Men.”

There are times when Biden plays to that stereotype. He memorably whispered to Obama, in front of cameras, that signing the health-care reform law was a “big [expletive] deal.” He publicly fretted about traveling in closed spaces during the swine flu scare. Most recently, he performed a short, embarrassing impersonation of an Indian call center operator.

The Republican National Committee has seized on Biden’s flubs. They have put out press releases about Biden calling attention to a “three-letter word: jobs — J-O-B-S,” and for appearing to empathize with China’s one child per family policy. But since Biden is not running for president anymore, his gaffes for the most part amount to an endearing trait that complements the preternaturally cool president.

On Capitol Hill, there is a prevailing sense among congressional leaders that Biden is someone they can talk to. “When I think of calling somebody in the administration, I’ll call Joe,” said Sen. Lindsey Graham, a Republican from South Carolina. He said Biden sometimes presents himself as being vexed by his own administration’s approach to the Hill, including its legislative strategy for passing the health-care law. Graham recalled the vice president occasionally calling to say, “ ‘I’m going to talk to you about A. But you know how I really feel about A’. Or sometimes he will say, ‘I’m going to talk to you about A, but it would be helpful if you said this. It would be nice if somebody up here heard the other side of the argument.’ ”

Many of the friendships Biden made in his Senate days have proven mutually beneficial.

Biden’s success in helping reach a lucrative film distribution deal with the Chinese government did not go unnoticed by Chris Dodd, a former senator from Connecticut, a Biden pal and the head of the Motion Picture Association of America.

Dodd said the deal went a long way with disgruntled Hollywood donors. “Well, it doesn’t hurt,” he said with a laugh.

In the recent debate over contraceptive policy, Biden raised early alarm bells that employers associated with religious institutions such as the Catholic Church would not abide by a mandate forcing them to provide contraceptives against their beliefs. Obama overruled him. But when the issue blew up, his private opposition emerged in press reports as the administration’s public voice of reason. “The ultimate resolution to this problem is where it should have been in the first place,” Biden told a crowd at Iowa State University, adding, “It got screwed up in the first iteration.”

As a campaigner, the incessantly emoting vice president can seem like the antithesis of the hyperintellectual president. He embraces bumper-sticker phrases (“Osama bin Laden is dead and General Motors is alive,” he told donors in Texas.) He talks tough with cops and soldiers. (On Veterans Day, he called Afghanistan a “God-awful moonscape” and “Godforsaken piece of real estate.”) He reminds teachers that his wife, Jill, still teaches community college, and he lays avuncular hands on the heads and shoulders of kids. (“I used to stutter, I used to t-t-tau-t-ta-talk l-l-l-lllike that,” he said before showing pictures of his dog to fourth-graders in York. “It was so embarrassing. . . . Everybody thinks you’re dumb.”) And it is Biden who feeds the base red meat. (“Your logo has been a horse’s head,” he told Teamsters in Las Vegas, before proposing that the Republican “logo should be the horse’s other end.”)

As the election year enters a more combative phase, so has Biden. On Monday night, he spoke at a fundraiser at the Georgetown garden of John and Teresa Heinz Kerry. He wagered that Democrats would win back the House, noting that he — whom he touted as “not a bad politician” — would visit all the contested districts. He invoked his “grandpop.” He juiced his sentences with “man” and “damn.” And he channeled real America to the power players dining on ten-thousand-dollar steak and potatoes. Republicans, he said, “don’t have a sense of what the average folks out there need,” and they “don’t get what it means to be middle-class.”

Florida senator Bill Nelson, who met with the vice president last month in the White House to solicit his help in extracting money and votes from the crucial swing state, suggested that Biden connected differently than the president. “People genuinely love Joe,” he said.

* * *

On Wednesday afternoon in the Benjamin Franklin State Dining Room at the State Department, Biden and Hillary Clinton stood onstage together flanking the British prime minister, David Cameron.

When it came time for Cameron to speak, he said a nice sentence or two about Biden, honoring him “as a legislator, as a statesman and as a campaigner.” Then he paid a lengthy tribute to Clinton.

Since at least June 2010, the great mentioners in the Washington press corps have floated the rumor that Biden might be replaced on the ticket by Clinton. The notion of “the Great Switcheroo,” as New York Magazine coined it, has received oxygen from stubborn Hillary supporters and some donors. Clinton insiders assured that the talk was coming from the Democratic base, not the Hillary inner sanctum. And it noticeably died down once the president’s approval ratings started rising.

“That came up less as a reflection on Biden than of the sense that somehow Hillary would bring some magic to this,” said Axelrod, who, like people close to Biden, described the speculation as “irritating.” He said that while Clinton had been a “spectacular secretary of state, and world-class politician,” the chatter was a “case in which people project onto Clinton transformative powers here that aren’t realistic.”

Also, Axelrod said, the story line “presupposes that the president is someone who would discard a guy who has been faithful and helpful,” and added that the affection and respect the two men share is “palpable.”

On the day Biden’s son Beau, the Delaware attorney general, suffered a stroke, Axelrod was briefing Obama in the Oval Office. Joe Biden had nearly died from a cranial aneurysm in 1988, and blood clots had probably claimed the life of his grandfather and grandmother. As Obama’s aides went over the business of the day, the president stared blankly at the window. He turned to Axelrod, and said, ‘I just don’t know how Joe is going to go on if this doesn’t work out well.’ ” When Biden returned to the White House, Obama walked to his office and embraced him.

From Biden’s end, there is no question that he wants to keep his job. When he visited York, a fourth-grader named Oliver Brown asked Biden how long he wanted to be vice president. Biden laughed.

“Good question, Oliver,” he said, standing in the middle of the classroom. “I want to do this job for another five years. Because as you know, presidents and vice presidents get elected for four years. And every four years you go back to the American people and you say, ‘Okay, this is the job we did, and this is the job the other guy wants to do. Now who do you want to pick?’ ”

* * *

“I must tell you, Mr. Prime Minister, and the secretary knows this, and friends like John Kerry know it — in my family, it wasn’t the War of 1812 that bothered anybody,” Biden said at Wednesday’s state luncheon, dipping back into the lineage that James Petty, his Salt Lake City genealogist, had helped trace. “The Bidens emigrated from Liverpool in 1825. But the other side of the family, the Finnegan side,” Biden said, pausing as the laughter in the crowd acknowledged the half of his heritage traditionally antagonistic to the British, “they had a different problem.”

Biden lifted his hands to the ceiling and invoked his grandfather.

“Ambrose Finnegan,” he shouted to the chandeliers, “things have changed.”