WASHINGTON — The president needed the senator from West Virginia on his side, but he wasn’t sure he needed his vice president to get him there.

It was summertime, and President Biden was under immense pressure to win the support of Senator Joe Manchin III, whose decisive vote in a 50-50 chamber made him the president’s most delicate negotiating partner. Mr. Biden had invited Mr. Manchin to the Oval Office to privately make the case for his marquee domestic policy legislation. Just before Mr. Manchin arrived, he turned to Vice President Kamala Harris.

What he needed from her was not strategy or advice. He needed her to only say a quick hello, which she did before turning on her heel and leaving the room.

The moment, described as an exchange of “brief pleasantries” by a senior White House official and confirmed by two other people who were briefed on it, was a vivid reminder of the complexity of the job held by Ms. Harris: While most presidents promise their vice presidents access and influence, at the end of the day, power and responsibility are not shared equally, and Mr. Biden does not always feel a need for input from Ms. Harris as he navigates some of his most important relationships.

In Ms. Harris’s case, she came to the job without strong ties to key senators; one person briefed on the Oval Office meeting said it would be more productive if the discussion between Mr. Biden and Mr. Manchin remained private. It is unclear that the president had much sway on his own, either, given the senator’s decision this week to break with the White House over the domestic policy bill.

But without a headlining role in some of the most critical decisions facing the White House, the vice president is caught between criticism that she is falling short and resentment among supporters who feel she is being undercut by the administration she serves. And her allies increasingly are concerned that while Mr. Biden relied on her to help him win the White House, he does not need her to govern.

“I think she was an enormous help to the ticket during the campaign,” said Mark Buell, one of Ms. Harris’s earliest fund-raisers since her first race for district attorney in San Francisco. “I would like to see her employed in the same way, now that they’re implementing their objectives or goals.”

The urgency surrounding her position is tied to whether the president, who at 79 is the oldest person to hold the office, will run for re-election in 2024. He told ABC News on Wednesday that he would run again if he was in good health. But questions about Ms. Harris’s readiness for the top job are starting far earlier than is usual for an administration in its first year.

Ms. Harris declined requests for an interview, but White House officials said that her relationship with Mr. Biden is a partnership.

“The vice president has diligently worked alongside the president coordinating with partners, allies and Democratic members of the House and Senate to advance the goals of this administration,” said Sabrina Singh, Ms. Harris’s deputy press secretary.

An early front-runner whose presidential ambitions fizzled amid a dysfunctional 2020 campaign, Ms. Harris was pulled onto the Biden ticket for her policy priorities that largely mirrored his, and her ability as a Black woman to bolster support with coalitions of voters he needed to win the presidency. But according to interviews with more than two dozen White House officials, political allies, elected officials and former aides, Ms. Harris is still struggling to define herself in the Biden White House or meaningfully correct what she and her aides feel is an unfair perception that she is adrift in the job.

Faced with declining approval ratings, a series of staff departures and a drumbeat of criticism from Republicans and the conservative news media, she has turned to powerful confidantes, including Hillary Clinton, to help plot a path forward.

Ms. Harris has privately told her allies that the news coverage of her would be different if she were any of her 48 predecessors, all of whom were white and male. She also has confided in them about the difficulties she is facing with the intractable issues in her portfolio, such as voting rights and the root causes of migration. The White House has pushed back against scathing criticism on both fronts, for what activists say is a lack of attention.

“I think it’s no secret that the different things she has been asked to take on are incredibly demanding, not always well understood publicly and take a lot of work as well as a lot of skill,” Transportation Secretary Pete Buttigieg said in an interview. “You have to do everything except one thing, which is take credit.”

Even in the best of times, the constraints of the job often make the vice president an afterthought, and not everyone asked to serve accepts it. (“I do not propose to be buried until I am really dead and in my coffin,” Daniel Webster, a former secretary of state, said in the 1840s about declining the job.)

But the complexity of the issues she has been assigned, and the long-term solutions they require, should have prompted the West Wing to defend Ms. Harris more aggressively to the public, said Representative Karen Bass, Democrat of California and the former chairwoman of the Congressional Black Caucus.

“What the White House could’ve done is been clearer with the expectations of what was supposed to happen under her watch,” she said.

Other Democrats say their frustrations run deeper.

Ms. Harris, who spent much of her four years in the Senate running for the presidency, was at odds with Mr. Manchin after she gave a series of interviews in West Virginia that he interpreted as unwelcome infringement on his home turf. Asked about the meeting in the Oval Office over the summer, a spokeswoman for Mr. Manchin said that the senator enjoys “a friendly and respectful working relationship” with the vice president.

Representative Henry Cuellar, a moderate from Texas and one of the more prominent voices on border issues in the Democratic Party, said his experiences with Ms. Harris’s team had been disappointing. When Mr. Cuellar heard Ms. Harris was traveling to the border in June, he had his staff call her office to offer help and advice for her visit. He never received a call back.

“I say this very respectfully to her: I moved on,” Mr. Cuellar said. “She was tasked with that job, it doesn’t look like she’s very interested in this, so we are going to move on to other folks that work on this issue.”

In the future, Mr. Cuellar said he would go straight to the West Wing with his concerns on migration rather than the vice president’s office.

Of the White House, Mr. Cuellar said, “at least they talk to you.”

Ms. Harris’s aides have pointed to her work lobbying other countries and companies to join the United States in a commitment to invest about $1.2 billion to expand digital access, climate resilience and economic opportunity in Central America. But little progress has been made on curbing corruption in the region.

On voting rights, Ms. Harris, who asked Mr. Biden if she could lead the administration’s efforts on the issue, has invited activists to the White House and delivered speeches. But her office has not developed detailed plans to work with lawmakers to make sure that two bills that would reform the system will pass Congress, according to a senior official in her office.

Since arriving in Washington, Ms. Harris has sought the counsel of other women — including Mrs. Clinton, the first female Democratic presidential nominee — who have achieved historical political success to help her find a path.

“There is a double standard; it’s sadly alive and well,” Mrs. Clinton said in an interview. “A lot of what is being used to judge her, just like it was to judge me, or the women who ran in 2020, or everybody else, is really colored by that.”

The two speak every few months on the phone; in November, Mrs. Clinton visited Ms. Harris in her West Wing office.

Ms. Bass pointed out that the double standard goes beyond Ms. Harris’s gender.

“I know, and we all knew, that she would have a difficult time because anytime you’re a ‘first,’ you do,’” Ms. Bass said. “And to be the first woman vice president, to be the first Black, Asian woman, that’s a triple. So we knew it was going to be rough, but it has been relentless, and I think extremely unfair.”

Before her trip to Vietnam and Singapore in August, Ms. Harris called Mrs. Clinton and several former female secretaries of state, including Condoleezza Rice and Madeleine Albright. She has had several private conversations with Angela Merkel, who has recounted the challenges she faced as the first female chancellor of Germany.

For this article, Ms. Harris’s office supplied dozens of examples of her work. She was sent to France to further repair frosty relations after an embarrassing diplomatic spat, a trip that the White House has hailed as a success. She has attended over 30 events focused on promoting the president’s domestic agenda, and her mark is on the final infrastructure bill on issues like clean water policy, broadband access and investments to combat wildfires. (Voting rights is another.)

The president also gave Ms. Harris credit for her interest in relieving student loan debt as he agreed on Wednesday to extend a moratorium on federal loan repayments until May 1, a decision that was hailed by activists and Democratic lawmakers who have pleaded with the administration to do more.

And yet, as the White House struggles to push through major legislation, Mr. Biden has relied on his own experience — 36 years in the Senate and eight years as vice president — to try to pull the United States out of the coronavirus pandemic and deliver on a towering set of economic promises. And Ms. Harris is facing questions about where she fits into the White House’s biggest priorities.

By all accounts, she and the president have a warm relationship. In meetings, the two often play off each other, with Mr. Biden allowing her to jump in and ask questions that go beyond what he has asked for; one adviser likened it to them playing “good cop, bad cop.” Alongside the president, Ms. Harris, a former prosecutor, has quizzed economic experts and immigration officials, at times asking them to better explain their reasoning.

Still, her allies are concerned that she is sometimes treated as an afterthought.

When the president worked late hours on a Friday night last month to win approval from lawmakers for his bipartisan infrastructure plan, a White House statement said only that he was working with a group of policy and legislative aides.

The vice president’s team, surprised her name had been omitted, informed the news media that she had also been there, placing calls to lawmakers. Asked about the exclusion, a White House spokesman said the initial statement issued to the public was based on information gathered before the vice president had arrived to join Mr. Biden and his senior staff. The White House issued a statement hours later noting Ms. Harris’s presence.

In recent weeks, she has seen a string of departures from the communications office; a number of other officials departed earlier this year.

Gil Duran, who worked for Ms. Harris when she was California attorney general in 2013, said she could be insulting and unprofessional. Mr. Duran said he quit after five months on the job when Ms. Harris declined to attend a briefing before a news conference, but then berated a staff member to the point of tears when she felt unprepared.

“A lot of us would still be with her if she was the Kamala Harris we thought she would be,” Mr. Duran said.

The White House had no comment when asked about the episode.

Aware of the criticism of her, Ms. Harris has been focused on promoting her own agenda in a series of interviews and appearances.

But Ms. Bass said the immediate challenge was the midterm elections next year, when Republicans could take back control of the House. But as for Ms. Harris’s presidential ambitions?

“I think she is the front-runner,” Ms. Bass said. “I think she’ll be the front-runner.”