She was there when he hosted Democratic governors at the White House, and she was on the line when he called Israel’s prime minister, and she was at his side on the balcony overlooking the South Lawn when he celebrated the Fourth of July. As the fireworks were about to start, he grabbed her hand and thrust it into the air in a gesture of unity.

In these days of uncertainty at the White House, Vice President Kamala Harris is sticking close to President Biden physically and politically, determined not to let anyone say that she has been anything other than completely loyal. But as a result, it means that the person who may have to step up if he steps down cannot be seen doing anything to prepare for the challenge of a lifetime.

With Mr. Biden’s future on the line, perhaps no one is in a more delicate position than Ms. Harris. For the first time since she took the oath as vice president in January 2021, Democrats are giving her a serious second look, with many coming around to the idea that she could potentially lead the party in November. As a practical matter, though, she has to ignore the chatter and disclaim any interest unless Mr. Biden reverses course and passes her the baton.

“She’s in an awkward position,” said the Rev. Al Sharpton, the civil rights leader, who spoke with Ms. Harris on Friday night at the Essence Festival of Culture in New Orleans. “But the job of vice president is awkward.”

Ms. Harris’s advisers adamantly maintain that she is doing nothing to get ready in case she suddenly has to kick off a campaign for president from a standing start, and there is no known evidence to the contrary. But Democrats acting with her interest at heart, even if not with her permission, are quietly gaming out what a Harris campaign might look like.

If Mr. Biden were to pull out of the race, as some Democrats are urging, there are two main scenarios for Ms. Harris. Assuming he does not resign outright, making her the sitting president, he could directly endorse her as the party’s candidate against former President Donald J. Trump and throw his weight behind securing her the nomination at the Democratic National Convention next month.

Other Democrats might still take a shot at the nomination, but it would be hard to overcome the advantage she would have if Mr. Biden openly urged his pledged convention delegates to back her. In the second scenario, however, he might simply leave it to the delegates to decide the nominee, opening the door to a more competitive and volatile weekslong scramble.

Speculation is already growing on possible running mates if she were to win. Ms. Harris would be the first Black and Asian American woman nominated by a major party, and in the cold, identity-driven logic of modern politics many assume she would need to balance her ticket with a white man, preferably one not seen as too liberal.

Two people close to the Biden-Harris team said an emerging favorite was Gov. Roy Cooper of North Carolina, a Southern moderate who has to work with a Republican legislature in a state that some Democrats have thought they might be able to flip in November. Ms. Harris and Mr. Cooper got to know each other when each was attorney general of their states.

Others often mentioned by people close to the Biden-Harris campaign include Govs. Andy Beshear of Kentucky and Josh Shapiro of Pennsylvania. Mr. Beshear impressed many national Democrats by winning a second term in a conservative state last year, while Mr. Shapiro could theoretically help Democrats capture Pennsylvania, a battleground critical to victory in November. But Kentucky is not seen as a likely pickup and Mr. Shapiro has been in office less than two years.

How Ms. Harris herself might view such calculations remains conjecture at the moment. The message from her office has gone out to members of her staff, donors and allies: No speculating, no chitchat. It will only hurt her, not to mention the president. She understands that she cannot be involved even in private discussions of this sort, allies said, because it would invariably leak and make her look disloyal to Mr. Biden.

“No one is having any conversation like that,” said Donna Brazile, a former Democratic National Committee chair. “And I know just based on the conversations I’ve had and the conversations I know others have had. She is standing, sticking. She respects the president; she will stand with the president. She is comfortable with the president. It is not happening. No one has dispatched someone like myself.”

Mr. Sharpton said that during his conversation with Ms. Harris on Friday night, she gave no indication of making plans. Still, he said he believed others were thinking ahead on her behalf. “I think there are some that are independent of her that are getting ready,” he said. “Some of them are saying they’ve got no signal from her, like I didn’t. But there are people being prepared just in case.”

If Ms. Harris is intent on proving her loyalty to Mr. Biden, there is concern in her circle about whether his advisers are reciprocating. Some Harris allies are acutely suspicious that some Biden allies are trying to save him by telling wavering Democrats that they cannot abandon him because they would then be stuck with a vice president who could not win in November.

Ms. Harris does not publicly entertain any of that. Instead, she has offered herself up as a one-woman validator, reassuring nervous Democrats about the president even as she implicitly makes the case for herself through her own performance.

“I see Joe Biden when the cameras are on and when the cameras are off; in the Oval Office, negotiating bipartisan deals,” she told a campaign rally in Las Vegas the day after Mr. Biden’s debate with Mr. Trump. “I see him in the Situation Room, keeping our country safe; on the world stage, meeting with foreign leaders who often ask for his advice. Joe Biden is a leader who always fights for the people of our nation. He fights, and he wins. And he wins. And he wins.”

Ms. Harris is not the first vice president to feel the conflict of sticking by the president who named them while nursing their own ambitions for the office. Being vice president is inherently a job caught between, the only person other than the president elected nationally and yet with power largely derivative from the top of the ticket. In the famous words of John Adams, the first to serve in the post, being vice president means that “I am nothing, but I may be everything.”

The sensitivity has been particularly distinct at certain moments in history. Vice President Gerald R. Ford made a point of demonstrating unyielding loyalty even as the Watergate scandal increased pressure on President Richard M. Nixon to resign. So did Vice President Al Gore when President Bill Clinton was impeached and faced pressure to step down for lying under oath about an extramarital affair.

Mr. Ford and Mr. Gore each understood that any perception to the contrary would be deeply damaging. But loyalty had its costs too. Mr. Ford ultimately pardoned Mr. Nixon, a deeply unpopular act that may have cost him the 1976 election. Mr. Gore was given a lot of grief for declaring on the day of Mr. Clinton’s impeachment that he would still “be regarded in the history books as one of our greatest presidents.” Mr. Gore lost his own presidential campaign in 2000 and blamed it at least in part on Mr. Clinton’s scandal.

“The worst thing a vice president can do at this point is to be anxious to get the president out,” said Elaine Kamarck, a former aide to Mr. Gore now at the Brookings Institution. “It just totally backfires. My guess is some fairly unsophisticated people are calling up Kamala Harris saying: ‘Can I do this? Can I do that?’ And if she’s smart, she will shut that down tight.”

One challenge for Ms. Harris is that she does not have a well-established national political organization of her own to turn to if the opportunity arises. Her own presidential campaign in 2020 collapsed before the first primary.

But those close to her expect she would inherit the Biden-Harris organization and the Democrats’ $240 million bank accounts if Mr. Biden does drop out, either before the nomination or certainly after it if she were to get the nod. While she would presumably install a few of her own most trusted people at the top of the campaign, she would be running the race that Mr. Biden started but could not finish.

In the meantime, she will keep hitting the road, campaigning in Las Vegas again on Tuesday, Dallas on Wednesday and Greensboro, N.C., on Thursday, delivering Mr. Biden’s message to everyone who will listen — and waiting to see if she goes, as Adams did, from nothing to everything.

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