Vice President Joe Biden points at President Barack Obama during the State of the Union address in Washington, Tuesday. (Evan Vucci/AP)

The Obamas had a mantra during the 2008 campaign when it came to those vying to get into their inner circle: “No new friends.” As the president enters the final year of his second term, at least one person has managed to defy that rule: Vice President Joseph R. Biden Jr.

On Tuesday night, President Obama made a policy announcement during his State of the Union address that was distinctly personal: putting Biden “in charge of Mission Control” for “a new moonshot” to cure cancer. It was a cause the vice president had taken up after the disease killed his eldest son, Beau, last year.

“For the loved ones we’ve all lost, for the families we can still save, let’s make America the country that cures cancer once and for all,” Obama said before looking back at Biden, seated behind him.

“What do you say, Joe?” he ­ad-libbed cheerily. “Let’s make it happen.”

The vice president, struggling to maintain his composure, mouthed “Thank you.”

Jill Biden, wife of Vice Presidet Joseph Biden, left, hugs First Lady Michelle Obama as she arrives for President Barack Obama's State of the Union address. (Drew Angerer/Bloomberg)

The initiative marked the second time in two days Americans had gotten a glimpse of how close the two men have grown over the past 7 1 /2 years. In an interview with CNN on Monday night, the vice president revealed that as he worried about supporting his son’s family after Beau Biden suffered a stroke in 2010, Obama offered to give his vice president money to ensure that he and his wife, Jill, did not have to sell their home in Wilmington, Del.

The extraordinary offer — which Biden said Obama would be “mad” at him for revealing — speaks to the unique personal relationship the men have developed during their time in office. Several other presidents established strong professional rapports with their seconds-in-command, collaborating on shared policy visions and deputizing them to spearhead key projects. But none of them has displayed such visible affection toward each other, in public as well as in private.

Biden has helped shape some aspects of the administration’s agenda, reinforcing Obama’s tendency to avoid military intervention in Middle East conflicts and working to shape the White House’s gun-control policy. But his most important role might be to offer the president a close friendship in a town from which he remains largely detached.

“We’ve never had that between a sitting president and a vice president in recent times, one where the friendship and familiarity factor was sky-high,” said Douglas Brinkley, a professor at Rice University and presidential historian. Biden, Brinkley added, fills “the need for the president to be able to talk out loud about one’s own mind, to be a sounding board.”

There are reasons to be wary of the presidential-buddy movie narrative — Bill Clinton and Al Gore were close until they weren’t, and the same can be said for George W. Bush and Richard B. Cheney.

“The nature of these personal relationships are very hard to tell,” said David Greenberg, author of “Republic of Spin: An Inside History of the American Presidency” and a history professor at Rutgers University. “Almost every vice president since Nixon has been described as being a more important player than any of his predecessors.”

In fact, President Jimmy Carter and Vice President Walter Mondale consciously sought to redefine the role of the office, a deal they struck in December 1976 during an evening conversation at Blair House. Richard Moe, who became the vice president’s chief of staff and codified the agreement in a memo, said it included giving Mondale total access to both the president and the information flow in the White House, as well as an office in the West Wing.

Biden, whose first Senate office was across the hall from Mondale’s, sought the former vice president’s advice several times during the 2008 presidential transition so he could replicate that seminal relationship. Moe said that while both Carter and Mondale see the more muscular, modern vice-presidential role “as part of their legacy,” Obama and Biden boast “the closest relationship” of anyone to occupy those two roles.

Part of it stems from Biden’s particular personality. He’s a hugger, and even the president is not off limits from his overtures. He was not closely allied with the Clintons, which made him both ideologically and personally, in Brinkley’s words, “an Obama Democrat.” And he has suffered acutely, both early in life with the loss of his first wife and daughter and in May, when his son succumbed to cancer.

When Beau Biden first had a stroke and faced the prospect of stepping down as Delaware’s attorney general, the vice president said to CNN’s Gloria Borger, he told Obama during one of their weekly private lunches that he was unsure how his son’s family would absorb the loss of that annual salary.

“I said, ‘But Jill and I will sell the house. We’ll be in good shape,’ ” Biden recalled, saying the comment prompted a fierce reaction from his dining companion. “He got up and he said: ‘Don’t sell that house. Promise me you won’t sell the house. I’ll give you the money. Whatever you need, I’ll give you the money.’ ”

Beau Biden recovered from that stroke and served out his term as attorney general. But he was hospitalized at MD Anderson Cancer Center in Texas in November 2013 and died a year and a half later at age 46.

Obama gave the eulogy at Beau Biden’s funeral, telling the Biden family that day, “We are here to grieve with you, but more importantly, we are here because we love you.”

Four and a half months later, Obama stood silently at the Bidens’ side in the Rose Garden as the vice president announced he would not seek his party’s 2016 nomination.

It is a story line that would have been hard to predict not only during the 2008 Democratic primary season, when Biden gave a backhanded compliment to his then-rival for being “articulate,” but also when he got the position of being Obama’s running mate.

As Greenberg observed, when a campaign selects a vice-presidential nominee, “the choice is informed by a political calculus in a way which no other presidential appointment is. They’re actually trying to think, ‘Who’s going to help you win the election?’ ”

“A person who you want to have as a close friend or confidant,” he added, “ranks pretty low in the selection process.”