WASHINGTON >> As President Barack Obama reviewed the comedy routine he was to deliver at the recent White House Correspondents’ Association dinner, one joke struck him as too hot. It suggested he might dump Vice President Joe Biden from the ticket.

“Four years ago, I chose Joe Biden as my running mate,” Obama was to say, according to people familiar with early drafts of the planned remarks. “Four years later, I’m almost positive I’m going with Joe again.” He would then affect an exaggerated wink for the audience. But the president instructed his speechwriters to cut the line, figuring it would only inflame speculative blather from Beltway busybodies about his vice president’s standing.

Biden is also a bit raw on this topic. It goes to an essential insecurity that haunts almost every No. 2 — a job that the back-slapping, shoulder-squeezing, muscle-car-loving Biden was wary of in the first place.

Biden, 69, delights in speaking bluntly — even as that can complicate things sometimes for the White House, as it did Sunday when Biden said he was “absolutely comfortable” with same-sex marriage (an endorsement that went beyond Obama’s statements on the issue).

He loves to remind people he did not have a boss for 36 years in the Senate, where he prided himself on being “my own man.” He would tell aides and Senate colleagues that “my manhood is not for sale” if he felt pushed around. He told friends he feared that the vice presidency could be “emasculating.”

As he embarks on what could be his last campaign, Biden is also concluding a sometimes uneasy term, one marked by triumphs and occasional tensions with a boss markedly different in style and temperament. Almost by definition, his job is amorphous.

“Being a vice president is kind of like being a first lady,” Secretary of State Hillary Rodham Clinton said in an interview about Biden. “You are there to support and serve the president. There is no job description.”

What job description there is often involves making the president look good. In recent weeks, Biden has given a series of heavily promoted policy speeches and assumed a strike-dog position in going after Mitt Romney, the presumptive Republican presidential nominee.

Aides to Biden love to point out all the quality time he and the president spend together — including a golf outing last month — to accentuate their working bond. (In his retelling of events, Biden always seems to be walking out of meetings with the president.)

Still, Biden’s effort to subordinate his own voice (or manhood) to the broader enterprise has been a struggle.

“In the good old days when I was a senator, I was my own man,” Biden told reporters last December on Air Force Two. “But now whatever I say is attributed to the administration. I finally learned that.”

He received a refresher course Sunday after saying on NBC’s “Meet the Press” that he was “absolutely comfortable” with same-sex marriage, an endorsement that went beyond Obama’s statements on the issue. Administration officials spent the next few hours making “clarifications” to Biden’s remarks, setting off a fresh round of grumbling inside the White House about Biden’s message indiscipline.

“Not helpful” is how one top Obama aide put the episode.

As with any union of opposites, the one between the rambling vice president and his cautious boss has required time, patience and adjustments.

Early on, for instance, it would drive Obama nuts to stand onstage waiting for Biden to introduce every dignitary in the room. So the president dispatched a top aide, Valerie Jarrett, to relay his displeasure to Biden’s office, according to top aides to both men. They initiated a fix: In future joint appearances, the president would remain offstage until the verbose vice president finished talking.

For his part, Biden was annoyed by what he regarded as a slight by Obama. When Biden curiously told House Democrats that even if the administration did everything right, “there’s still a 30 percent chance we’re going to get it wrong,” Obama responded to a reporter’s question by saying he did not know what Biden was referring to. He tacked on a “not surprisingly” for good measure.

At their next weekly lunch meeting, Biden complained that the quip was disrespectful, according to White House aides. Obama apologized but expressed his own frustration about Biden’s verbal misadventures — called “Joe bombs” by some staff members during the 2008 campaign. Advisers describe the session as a tense but necessary clearing of the air that allowed them to move forward.

A UTILITY PLAYER

Over time, White House officials say, both principals — whose ages are separated by more years (19) than their West Wing offices are steps (17) — have learned to adapt for the betterment of the alliance. Biden has worked to restrain his ego in the service of his support role — “a total utility player,” as Clinton described Biden, or “the guy who does a bunch of things that don’t show up on the stat sheet,” as Obama once put it.

The president has come to appreciate Biden’s loyalty, tested over a whiplashing term, and has deployed him as a designated contrarian in debates. “There’s, I think, an institutional barrier sometimes to truth-telling in front of the president,” Obama said in a 2009 interview with The New York Times. “Joe, in that sense, can help stir the pot.”

Obama has also relied on his deputy for his political skills and complementary strengths. Obama might have “overestimated his own ability to engineer his own charm offensive, especially on the Hill,” said a former White House aide who asked not to be named while characterizing the president’s mindset.

“The vice president is proof that to some degree the path to the new school goes through the old school,” said Jared Bernstein, a former top economic adviser to Biden. He refers to Biden as “an ambassador back to an earlier form of politics where relationship-building plays a key role.”

Obama and Biden have arrived at what people close to both describe as a friendship, one of the few the president has made in office. They attend the sporting events of Obama’s daughter Sasha and Biden’s granddaughter Maisy, who attend the Sidwell Friends School together. When Biden’s son Beau suffered a stroke in 2010, Obama was one of the first to call. Michelle Obama has developed a warm relationship with Jill Biden, with whom she has worked on issues relating to military families.

But people close to them also allow that it is impossible to know what goes on in the privileged space between the country’s two highest-ranking officers — one of the most fraught and scrutinized relationships in any administration.

It “carries a Shakespearean dependency element about it,” said former Vice President Walter F. Mondale, who served under Jimmy Carter. Mondale also compared the partnership to “a four-year nondivorcable marriage,” though “at least you get to live in different houses.”

And the power dynamic skews totally to the top of the ticket. “A vice president thinks constantly about what the president must be thinking,” said Jack Quinn, who was chief of staff to Vice President Al Gore.

Now a lobbyist, Quinn notes a recurring line in the new HBO series “Veep” in which almost every time the frustrated No. 2 (played by Julia Louis-Dreyfus) walks into her office she asks, “Did the president call?”

‘REGULAR JOE BIDEN’

Biden is as easy a punch line as anyone is in Washington — a perma-tanned and gaffe-prone goofy uncle type with a smile that looks practiced in front of a mirror. He makes for brilliant fake headlines in The Onion (“Shirtless Biden Washes Trans Am in White House Driveway”) and easy late-night comedy (when Michelle Obama told David Letterman how her dog, Bo, puts his paw on her leg and starts barking, the host interjected, “Is that what Biden does?”).

Biden exhibits a level of self-deprecation that friends say is healthy for his job. Young audiences are oddly drawn to him the way the MTV generation supposedly swooned for Tony Bennett.

“I was kind of secretly hoping one of my kids would go out and make a million bucks,” the vice president joked to students at Howard University last month. Why? “So when they put me in a home, at least I’ll have a window with a view.”

Publicly imagining oneself “in a home” is not something politicians typically do. But you never know what you’re going to get with Regular Joe Biden. It is part of his charm and also his danger.

“He reminds me of a cool-cat Vegas headliner in ’65,” said Michael Murphy, a Republican media consultant. “Onstage with drink in hand: ‘To hell with the casino! We’re going all night.” (Biden, in point of fact, does not drink.)

Still, after nearly four decades in Washington and two presidential runs, Biden has a strong sense of his own stature. After ending his presidential campaign in January 2008, he was asked at a Capitol Hill fundraiser if he wanted to be considered for secretary of state. No, he said, he wanted to be offered the job — not audition for it. It was a respect thing.

He often recoils at being “handled” and has spoken bitterly— particularly during the 2008 campaign — about being kept out of the loop on strategy discussions. Obama’s top campaign aides were indeed hesitant to tell Biden too much, for fear of press leaks.

Some officials close to the president worry that Biden might become less restrained in sharing his personal positions — as he did Sunday on same-sex marriage — in the service of his own political ambitions.

Biden has not ruled out making a third run for president in 2016. You are either on your way up or on your way down, he has told aides, and to deny interest in moving up makes you seem less politically potent.

Solicitous and emotive, Biden is unquestionably well liked within the administration. “The nicest person in the cabinet,” Transportation Secretary Ray LaHood said.

He has displayed devotion to Obama, White House aides say, which has included impassioned defenses of the president in tense settings. In an appearance before House Democrats by Biden shortly after the party lost its majority in November 2010, the then-congressman (and not-yet-laughingstock for his racy tweets) Anthony D. Weiner charged that Obama was acting less like a leader and more like a negotiator — and a weak one.

“There is no goddamned way I’m going to stand here and talk about the president like that,” Biden boomed, according to White House and congressional officials who were present.

“I think what’s happened over three years is the president has come to appreciate the vice president’s loyalty and idiosyncrasies,” said Ronald A. Klain, a former chief of staff to Biden who held the same position for Gore. Both have become more mindful of the relationship and have worked on it.

It also helps, Klain said, that they each have their own friends, lives and interests.

“They haven’t tried to turn this into some sort of buddy movie,” he said.

© 2012 The New York Times Company