“The champagne of beers,” Ms. Harris joked, after Mr. Colbert noted that she had requested that brand of suds — which is brewed in the battleground state of Wisconsin.

During her taped appearance on “The Late Show,” Ms. Harris also dealt with far weightier subjects. Asked about the war in Gaza, an issue that could threaten her chances of winning states like Michigan, she suggested the conflict was unlikely to end soon, even as she urged optimism.

“We cannot lose some belief in the possibility” of a cease-fire, she said, adding that “the United States must work and not lose hope and not throw up our hands.”

And she condemned Mr. Trump — for the second time on Tuesday — over reporting from a new book by the journalist Bob Woodward that claimed that Mr. Trump had sent rare Covid test machines to Mr. Putin in the early days of the pandemic.

“I ask everyone here and everyone who is watching: Do you remember what those days were like?” Ms. Harris said, pointing out the number of Americans dying every day. “You remember how many people did not have tests and were trying to scramble to get them?”

The vice president’s appearance with Mr. Colbert capped a busy day of high-profile interviews, which she had almost entirely avoided during the rollout of her abbreviated campaign.

Earlier on Tuesday, she joined “The View” on ABC for a live appearance, putting forward a new proposal on home health care and accusing Mr. Trump of lacking “empathy on a very basic level.” Soon after, she gave a lengthy interview to the radio host Howard Stern that delved into fresh details of her life and personality.

On Monday, “60 Minutes” broadcast a hard-hitting segment featuring her and the journalist Bill Whitaker. And on Sunday, she appeared on the popular podcast “Call Her Daddy.” The wide range of interviewers reflects how the Harris campaign is trying to reach the many voters who get their news online and from nontraditional media with Election Day approaching.

The full interview with Mr. Colbert will be broadcast on CBS at 11:35 p.m. The traveling pool of journalists who accompany the vice president provided a transcript of excerpts from Ms. Harris’s appearance before it aired.

Her time on “The Late Show” had its lighter moments, too, as when Mr. Colbert asked what Ms. Harris was thinking during her debate against Mr. Trump when she archly put her hand to her chin in a moment that went viral.

“It’s family TV, right?” Ms. Harris replied. “It starts with a W, there’s a letter between it, then the last letter’s F.”

Erica L. Green and Katie Rogers contributed reporting.

This story will be updated.

That moment could arrive immediately, he said, or after Mr. Trump’s next term, if he wins, which Mr. Romney said he thought was the race’s more likely outcome. “I believe I will have more influence in the party by virtue of saying it the way I’ve said it,” Mr. Romney said, explaining why he was stopping short of the seemingly obvious next step of an endorsement for Ms. Harris. “I’m not planning on changing.”

Mr. Romney wrote in the name of his wife, Ann, for president in 2016. In 2020, he said he had not voted for Mr. Trump but would not say if he had voted for President Biden. On Tuesday, he joked that his vocal opposition to Mr. Trump left his audience to “do the very difficult calculation of what that would mean” in terms of his vote this year. Given his track record, the answer was far from clear.

Mr. Romney’s unwillingness to endorse Ms. Harris was a blow for her campaign, which has been pouring tens of millions of dollars into advertising aimed at anti-Trump Republicans. Mr. Romney, who voted twice to impeach Mr. Trump and who praised Ms. Harris after her debate performance against him, seemed like an obvious target.

Ms. Harris has gone out of her way to highlight endorsements from conservatives like former Representative Liz Cheney of Wyoming and her father, former Vice President Dick Cheney, who have potentially helped create a model for deeply conservative voters reluctant to support Mr. Trump to vote for a Democrat for the first time in their lives.

The answer was also a curious one for Mr. Romney, who announced in September that he would not seek re-election, saying that he wanted to make way for a “new generation of leaders.”

That retirement announcement was in some ways the culmination of a long divergence between Mr. Romney, a genteel and wealthy former governor with traditional conservative views, and the Republican Party, which has molded itself to fit Mr. Trump’s needs in recent years. That Mr. Romney still thinks there is a role for him to play in the G.O.P. hinted at an optimism about a turnaround in the party that few critics of Mr. Trump share.

Some Republicans said they understood Mr. Romney’s position. “All of those now pro-Kamala voices will not be allowed back in,” said Doug Heye, a Republican strategist. “But there will be a G.O.P. post-Trump, and there should be some sane people remaining to fix that.”

Mr. Romney has made no secret of his disgust for Mr. Trump, imploring donors and Republican candidates during this year’s G.O.P. primary to unite around someone else. When that did not happen, he said he could not vote for Mr. Trump in November because character mattered more than policy.

“When someone has been determined by a jury to have committed sexual assault, that is not someone who I want my kids and grandkids to see as president of the United States,” he told MSNBC, a reference to the civil case brought against Mr. Trump by the former magazine writer E. Jean Carroll.

Mr. Romney also holds Mr. Trump’s running mate, Senator JD Vance of Ohio, in particularly low esteem.

“I don’t know that I can disrespect someone more,” Mr. Romney told his biographer, McKay Coppins of The Atlantic, last year.

Mr. Stern is not a journalist, and he said multiple times that he supported Ms. Harris for president, but he is a skilled inquisitor who managed to extract an array of fresh details about her life.

Here is a (perhaps incomplete) list of new things we learned about Ms. Harris.

She is angry about the new reporting on Trump, Putin and Covid testing.

Ms. Harris seemed apoplectic at the idea — reported in a new book by Bob Woodward — that when Mr. Trump was in office, he sent rare Covid test machines to President Vladimir V. Putin of Russia.

“This guy who was president of the United States is sending them to Russia to a murderous dictator for his own personal use,” she said. “This person who wants to be president again who secretly is helping out an adversary when the American people are dying by the hundreds every day and in need of relief.”

She could not believe Trump’s behavior at their debate.

During their debate last month, Mr. Trump uncorked his false claim that Haitian immigrants in Ohio were eating their neighbors’ pets. Ms. Harris was just as stunned as everyone watching, she said.

“There were a couple of moments at least in the debate where it was surreal, honestly,” she said. “This was a very serious moment to earn the votes of the American people, and he was talking about things that were factually untrue and quite ridiculous.”

She is proud of putting ‘a lot of people in jail.’

“I have put a lot of people in jail” might be a bumper-sticker slogan for a law-and-order candidate. And in some ways, that is how Ms. Harris is aiming to brand herself in the campaign’s final month. She discussed at length her time as a prosecutor — and made a strikingly blunt acknowledgment of the outcome of many of her cases.

She is all too aware of the threats against her life.

Ms. Harris said she had faced death threats dating to her time as a local prosecutor, though she declined to speak about them. “I refuse to live in fear of the bad guys,” she said.

She thinks Trump is ‘getting punked’ by dictators.

Ms. Harris made clear she was simpatico with President Biden on foreign policy, especially when it came to backing Ukraine against the Russian invasion.

“I grew up in the neighborhood,” she said. “Some would say you’re getting punked if you stand in favor of somebody who’s an adversary over your friends on principles that we all agree on.”

She won’t reveal her cabinet choices unless and until she wins.

Mr. Stern predicted that the Republican whom Ms. Harris has pledged to place in her cabinet would end up being Liz Cheney, the former Wyoming congresswoman who last week appeared at a campaign rally with her in Wisconsin.

Ms. Harris would not take the bait.

“I gotta win, Howard,” she said. “I gotta win. I gotta win. And listen, but the thing about Liz Cheney, let me just say, she’s remarkable.”

She told Stern that talking to him was a form of therapy.

Mr. Stern noted that it remained taboo for national politicians to acknowledge that they seek the sort of therapy that millions of Americans rely on in their daily lives. He asked Ms. Harris if she was talking to someone to cope with the immense pressure of running for president.

“This is my form of therapy, right now,” she said. She went on to describe her longtime and robust circle of friends, her family and others on whom she counts for emotional support, then offered a bit of self-reflection about those she does not engage with.

“I choose,” she said, “not to have mean people in my life.”

She likes Formula One racing.

Ms. Harris is a fan of the Formula One car racing circuit, which has long been popular in Europe but has gained a foothold in the United States after a Netflix series ignited new interest.

Her favorite driver: “Lewis Hamilton, of course.”

She is mildly dismissive of her husband’s musical tastes.

Ms. Harris ribbed her husband, Doug Emhoff, for being a fan of the English pop band Depeche Mode, but said the artists they agreed on included Prince and U2.

“He and I have very different musical tastes, my husband and I,” Ms. Harris said. “Depeche Mode, that’s him. I grew up kind of hip-hop.”

She saw U2 play at the Sphere in Las Vegas.

Ms. Harris took Mr. Emhoff to see U2 play at the Sphere in Las Vegas. Ms. Harris seemed positively giddy in describing the venue — which she warned should be attended sober.

“Oh my God, have you been to the Sphere?” she asked Mr. Stern. “Everyone should go in with a clear head.”

Mr. Stern replied, “Basically, don’t be high.”

“Correct,” Ms. Harris said. “It’s a lot. There’s a lot of visual stimulation.”

She starts her morning on an elliptical machine, watching ‘Morning Joe.’

Ms. Harris said her morning workout routine typically involved 30 to 45 minutes on an elliptical machine, during which she watches “Morning Joe,” the anti-Trump MSNBC show that is also a favorite of Mr. Biden’s.

She eats raisin bran and Special K for breakfast.

In 2018, Ms. Harris told New York magazine that her breakfast routine involved low-sugar, generic raisin bran. She told Mr. Stern that she still liked the cereal — just not every morning.

“So I don’t eat raisin bran every morning,” she said. “You asked me what was my favorite cereal. I would put it right up there, OK?”

She also said she enjoyed Special K, a choice she admitted would “be obnoxious.”

She enjoyed Maya Rudolph’s impression of her.

Earlier, in an appearance on “The View,” Ms. Harris delivered a full laugh when shown Maya Rudolph’s impersonation of her from “Saturday Night Live.” The vice president reacted as if she had not seen Ms. Rudolph play her before.

To Mr. Stern, Ms. Harris praised the actor’s work.

“Well, I just saw it, actually, and it was funny,” she said. “I am a huge fan of Maya Rudolph, so I think she put a lot of time into doing the piece and the character.”

The flood of ads in races for the House, Senate and White House inflame cultural divisions and cast Democrats as outside the mainstream. They are a sign that Republican strategists believe they have found a potent third leg for their messaging stool in 2024, along with the mainstays of inflation and immigration.

Republicans are returning to a message that was tried, mostly unsuccessfully, in the 2022 midterms, as they attempt to motivate their base and curb their losses with female voters repelled by the party’s stance on abortion.

Mr. Trump’s most aired ad about Vice President Kamala Harris in recent weeks ends with the tagline: “Kamala is for they/them. President Trump is for you.”

In Ohio since the start of September, every ad about Senator Sherrod Brown from the leading Senate Republican super PAC has touched on transgender topics, such as accusing him of “allowing transgender biological males in girls’ sports.” Mr. Brown is one of the nation’s most vulnerable Democratic incumbents.

In Montana, five ads have deployed similar lines about transgender women in sports and bathrooms as Republicans press the case that Senator Jon Tester, another endangered Democrat up for re-election, is too liberal for the heavily Republican state.

“It’s one of the issues where Democrats are furthest from the center of the country,” said Brad Todd, a Republican ad maker who has produced commercials on transgender issues in multiple races this year. “They are doing something that is totally illogical to appease a tiny slice that is very radical in their base.”

Republicans acknowledge there are relatively few instances in which transgender athletes compete in youth sports. But they said highlighting the unwillingness of Democratic politicians to break with their party’s progressive wing on the issue was a powerful tool for depicting lawmakers as liberal or extreme.

Up and down the ballot, Democratic candidates have mostly tried to ignore the onslaught, preferring to pivot toward more favorable policy terrain, such as abortion, rather than to be dragged into public debates on transgender issues.

Privately, though, Democratic strategists concede that the transgender attacks are taking a toll in some races. The most aired Trump ad in recent weeks was rated as one of his campaign’s more effective in September in some Democratic testing, according to results reviewed by The Times.

Kelley Robinson, the president of the Human Rights Campaign, one of the country’s leading L.G.B.T.Q. advocacy groups, said Republican attempts to use transgender people as political tools had failed in key races in 2022 and 2023. She predicted they would fall flat again in 2024.

“It shows that Republicans are desperate right now,” Ms. Robinson said. “Instead of articulating how they’re going to make the economy better or our schools safer, they’re focused on sowing fear and chaos.”

Attacks on what Mr. Trump calls “transgender insanity” have reliably been one of his loudest applause lines at his rallies. But now Mr. Trump has shifted significant resources to move that message far beyond his most fervent fans.

In the last three weeks, Mr. Trump’s campaign alone has spent more than $15.5 million on two television ads that resurface comments Ms. Harris made in 2019 describing her support for policies that “every transgender inmate in the prison system would have access” to gender-affirming surgery.

Chris LaCivita, one of Mr. Trump’s two campaign managers, said what made the commercials potent was using Ms. Harris in her own words. “It doesn’t require any hyperbole,” he said. “It’s her.”

In that 2019 interview, Ms. Harris said she supported gender-affirming surgery for state prison inmates, and she expressed support in an American Civil Liberties Union questionnaire that year for gender-transition care, including surgery, for federal prisoners and detained migrants.

“She wants to do transgender operations on illegal aliens that are in prison,” Mr. Trump said at their debate last month.

The Harris campaign declined to comment.

Transgender-focused ads have been running in key Senate races, including in Montana, Ohio, Pennsylvania, Texas and Wisconsin. Many are from the Senate Leadership Fund, the super PAC aligned with Senator Mitch McConnell of Kentucky, the top Senate Republican.

Most of the Republican ads do not criticize the transgender community in general. Instead, they zero in on specific wedge cases, such as transgender women and girls in sports, transgender women’s sharing of locker rooms, the use of taxpayer funds for gender-affirming surgery for people in prison and access to transition services for minors, such as puberty blockers.

Leigh Finke, the first transgender member of the Minnesota House of Representatives and the executive director of the Queer Equity Institute, said the more narrow focus could make the attacks especially hard to address because they were more about emotion than evidence.

“There is no way for the data to show that trans inclusion is somehow a threat,” Ms. Finke, a Democrat, said, adding, “This is really an argument that is based on an impulse someone might feel. It’s hard to argue with someone’s feelings.”

Republican strategists said the focus on transgender women and girls in sports had been particularly effective with a key group of voters the party has hemorrhaged support from in recent years: college-educated suburban women.

“One of the things you see in the focus groups is the moms get really visibly angry on this issue,” said Jim McLaughlin, a Republican pollster who works for Mr. Trump and other Republican campaigns. “It’s a fairness issue. They don’t want their daughters to lose a scholarship, and they don’t want them to get hurt.”

Those are some of the recurring themes in the ads.

“It’s just wrong,” one mother says in a Republican ad in Wisconsin.

“It’s unfair and dangerous,” a grandfather says in a Republican ad in Ohio.

“Our girls’ sports are under attack,” another Montana mother says in an ad.

The Trump campaign placed its transgender ads in heavy rotation during football games in recent weeks, according to a person with knowledge of the ad-buying strategy. The popular radio host Charlamagne Tha God said on his show, “The Breakfast Club,” last week that the transgender commercial was especially striking because of when it aired.

“I don’t know if it was the backdrop of football, but when you hear the narrator say, ‘Kamala supports taxpayer-funded sex changes for prisoners’ — that one line, I was like, hell, no, I don’t want my taxpayer dollars going to that,” he said. “That ad was effective.”

It has helped Republicans that there have been high-profile examples of transgender athletes, especially the swimmer Lia Thomas, who in 2022 became the first transgender athlete to win an N.C.A.A. Division I title.

One of Ms. Thomas’s past competitors, Riley Gaines, narrated ads in the Missouri and Tennessee Senate races this year.

“Woke politics made me swim against a man,” Ms. Gaines says in the Tennessee ad.

A Gallup poll in 2023 showed that only 26 percent of Americans believed transgender athletes should be able to play on sports teams that fit their gender identity — a drop from two years earlier.

At the same time, polls routinely show that a majority of Americans believe society should accept transgender people for the gender they identify with, including in five presidential battleground states surveyed by The New York Times and Siena College: Arizona, Georgia, Michigan, North Carolina and Wisconsin.

That was also the case in Ohio, where 54 percent of voters agreed, and yet no one has faced a more relentless focus on the issue than Mr. Brown.

Mr. Brown’s campaign has been the target of what it estimated was $37 million in attacks on transgender issues, including all the ads from the Senate Leadership Fund since Labor Day. Reeves Oyster, a spokeswoman for Mr. Brown, said the senator agreed with the state’s Republican governor, Mike DeWine, that decisions about sports participation should be determined by local school districts, individual sports leagues and the state athletic commission.

In the presidential race, a pro-Trump super PAC began to echo the campaign commercial over the weekend with an ad of its own, calling Ms. Harris a “crazy liberal,” showing the same clip about surgery for prisoners and ending with the same “they/them” tagline. The ad featured an image of Jonathan Van Ness, the star of the show “Queer Eye,” wearing a dress. Mr. Van Ness has said he identifies as nonbinary.

“Coming after a renowned celebrity star that people love and adore that has been in our living room for years doesn’t seem like the right strategy to win hearts and minds,” said Ms. Robinson of the Human Rights Campaign.

Ms. Harris met with Mr. Van Ness and the “Queer Eye” cast in July. An image from that meeting appeared in a recent ad from the American Principles Project, a socially conservative advocacy group. Terry Schilling, the group’s president, said that in a dozen focus groups it conducted last year, it found that when it introduced the issue of minors and gender identity, liberal women were much less comfortable than they were with any other issue.

Mr. Schilling said the most effective ad his group had run in 2024 focused on Ms. Harris and her previous statements on transgender issues and that, when shown to viewers online, the 30-second ad had a completion rate of 91 percent, meaning 91 percent of viewers watched to the end and did not click the “skip ad” option.

“This is where Republicans can run the numbers up, make Democrats look extreme and also reach the base,” Mr. Schilling said. “It’s three birds with one stone.”

Jeremy W. Peters contributed reporting.

“It’s profound, and it is the height of irresponsibility and, frankly, callousness,” she said of Mr. Trump’s claims. “I fear that he really lacks empathy on a very basic level, to care about the suffering of other people and then understand the role of a leader is not to beat people down — it’s to lift people up.”

Ms. Harris also addressed reports that Mr. DeSantis had declined to take her calls this week as another storm barrels toward his state. She said it was important that federal, state and local agencies work together on disasters, and called it a “shame” that it had not happened.

“When I’m president, I will continue to call him to see what he needs for help,” Ms. Harris said of Mr. DeSantis, who has attacked the vice president’s outreach as politically motivated and said, “She has no role in this.”

Ms. Harris offered a warning to Floridians in the path of the approaching Hurricane Milton to follow the guidance of authorities on the ground and leave their homes if advised.

“I urge every and anybody who is watching or has family members in that area, please, please, please take seriously your local officials’ admonitions to you,” she said. “If they’re telling you to evacuate, get your stuff and go.”

The sit-down on “The View” was one of a series of friendly interviews that Ms. Harris is scheduled to do on Tuesday. She is set to chat with the satellite radio host Howard Stern in the afternoon and will then record an appearance on “The Late Show With Stephen Colbert,” which will air late in the evening.

Ms. Harris received a warm welcome from the hosts of “The View,” including a full-throated endorsement from Whoopi Goldberg. They asked her a broad variety of questions, including one about a specific way that her presidency would differ from President Biden’s.

She initially pointed to their differing life experiences and divergent policy focuses. But when pressed on whether there was anything she would do differently from her boss, she said, “There is not a thing that comes to mind.”

Trump campaign officials immediately seized on the remark, clipping the exchange and promoting it on their social media platforms.

Later in the interview, after pointing to her endorsements from Republicans, she did cite one potential move that would distinguish her from Mr. Biden: her promise to appoint a Republican to her cabinet.

During the appearance — her first live television interview since Mr. Biden dropped out in July and she became the Democratic nominee — Ms. Harris unveiled a new plank of her economic plan, which would extend Medicare coverage for long-term, at-home care for seniors. The plan is designed to reach the so-called sandwich generation — an estimated 105 million people, including plenty of undecided voters, who are caring for their aging parents while raising their own families.

“There are so many people in our country who are right in the middle,” Ms. Harris said. “They’re taking care of their kids, and they’re taking care of their aging parents, and it’s just almost impossible to do it all.”

Ms. Harris, who has also proposed a child-care tax credit, has spoken about her own experience caring for her mother while she was dying of cancer.

Joy Behar, another longtime host of “The View,” asked Ms. Harris a question on the minds of many Democrats perplexed at the possibility that Mr. Trump could return to the White House: How is this race so close?

“I personally cannot understand why anyone would vote for him,” Ms. Behar said.

Ms. Harris did not try to explain Mr. Trump’s appeal. Instead, she spoke about Republicans, including former Representative Liz Cheney of Wyoming, who are supporting her as a means to block Mr. Trump.

“People are exhausted now, and they’re exhausted with the lies,” Ms. Harris said. “They’re exhausted with the selfishness. They’re exhausted with the attempt to divide us as Americans. And they’re ready to turn the page and chart a new way forward. And I feel very optimistic.”

Her appearance came as a New York Times/Siena College poll released on Tuesday showed her slightly ahead nationally, and gaining an edge on Mr. Trump as the candidate most voters see as representing change and caring about people like them.

She tried to hone that message during her interview after a question about immigration, when she pointed to Mr. Trump’s successful torpedoing of a bill that would have poured resources into border security.

“He spends full time engaged in grievance about what has happened to him,” Ms. Harris said.

“But what he does not talk about is you,” she said. “He does not talk about what you need. He does not talk about what your parents need, what your children need.”

“There are so many people who are right in the middle,” said Ms. Harris on the ABC talk show.

She recalled caring for her mother, Shyamala Gopalan Harris, before she died of cancer in 2009. “It’s about dignity for that individual. It’s about independence for that individual,” she said.

Home health services that last more than a few months represent “the biggest gap in Medicare,” said David Grabowski, a health policy professor at Harvard who studies long-term care. Medicaid, the federal-state program for the poor, covers home care for elderly and disabled Americans who need it, but people are forced to spend all their savings to qualify and often face long waiting periods.

The Harris campaign said that the plan would be paid for with savings from the expansion of Medicare price negotiations with drug manufacturers, which is expected to lower government spending for older people’s prescriptions. But it is not clear how much the additional benefits under the Harris plan would cost.

“This would be transformative from a care perspective,” Mr. Grabowski said, but he added that the price could be very high. “There will be a lot of sticker shock once this is costed out.”

In a fact sheet published on Tuesday, the Harris campaign also endorsed expanding Medicare to cover vision and hearing benefits — proposals that have been floated before but rejected by Congress. Medicare, the federal insurance program for older Americans, does not cover such services, which many older people use. Some private Medicare Advantage plans offer it as an optional benefit.

Former President Donald J. Trump’s campaign said he previously supported the idea of covering home care in the Republican Party’s 2024 platform, where it appears in a sentence about “care at home for the elderly.”

“President Trump will take care of our seniors by shifting resources back to at-home senior care, overturning disincentives that lead to care-worker shortages, and supporting unpaid family caregivers through tax credits and reduced red tape,” said Karoline Leavitt, a campaign spokeswoman, in an email.

Millions of Americans struggle to find affordable home care for themselves or their loved ones as they age. Medicare does not cover longer periods of home care, typically paying for a home aide only when a patient is recovering from an acute medical condition, like a stroke, and only for a short time, often just a few months.

While Medicaid will pay for a home aide if someone has a low income and limited assets, there are long waiting lists. In many areas of the country, there is a severe shortage of workers because of low wages and better, less stressful jobs in other industries. Home health aides assist patients with basic daily tasks like dressing, eating and using the bathroom.

Most people have no choice but to rely on a family member to care for them because they cannot afford the cost of professional aides, which can surpass the expense of an assisted-living center. Agencies can charge some $30 an hour, according to Genworth, an insurance company for long-term care. Others end up spending their assets and moving to a nursing home, which Medicaid covers.

The number of Americans expected to need home care is expected to grow in the coming years. The first baby boomers have been entering retirement by the thousands every day, and they will begin turning 85 in 2031. While not everyone who reaches an advanced age requires long-term care, a substantial share of the very elderly need such help because of physical disability or dementia.

Expanding access is likely to require many more workers to provide the care.

“We cannot overstate that without staff, there is no care,” said Katie Smith Sloan, chief executive of LeadingAge, an association of nonprofit nursing homes and organizations that assist aging people.

Judith Feder, a professor of public policy at Georgetown University who published a recent paper on a possible Medicare home-care benefit, said such a policy would relieve financial and physical burdens on family members.

“It is what we need in national leadership to address a need among the population that has been disregarded for much too long,” she said.

The program could cost hundreds of billions of dollars or more, and it might face a difficult time in Congress. According to the Harris campaign, the program would be financed through aggressive negotiations over prescription drugs under Medicare and through other policies, including taxes on companies that shift jobs overseas.

Both expanded home health care and Medicare prescription-drug negotiations are popular ideas.

The Biden administration also wanted to create Medicare benefits for hearing and vision and offer more assistance for long-term care at home as part of its big domestic policy bill. But the efforts were axed from the bill during congressional negotiations when Democrats still controlled both the House and Senate. The Biden approach to home health care, estimated to cost $150 billion over a decade, was more modest. It would have provided additional funding to state Medicaid programs to reduce waiting lists for home care. The Harris proposal would be much broader because it would not be limited to Americans enrolled in Medicaid, who must be poor to qualify.

A Medicare benefit would be broader, though that does not mean it would be free to everyone.

The Harris campaign fact sheet said that the program would require payments from families on a sliding scale according to income.

A recent paper from the Brookings Institution sketched out possible options for a Medicare home-care benefit, including higher contributions from wealthier families and restrictions on paying family members to provide the care. Its plan, with a benefit targeted at lower-middle-class Americans, was estimated to cost around $40 billion a year, and the campaign fact sheet cited that number. A more generous program could far exceed that estimate.

“The costs are a very major consideration,” said Mark J. Warshawsky, a senior fellow at the American Enterprise Institute and the former vice chairman of an Obama-era commission on long-term care. “Medicare, because it is a universal benefit, is not the right way to provide it, because many people can afford the care they have with the assets they have, the income they have and their supports from family. It’s very poorly targeted.”

Previous federal efforts to address long-term care at home have foundered. Democrats tried to create an insurance plan that would. include longer coverage for home care for as part of the Affordable Care Act, but it was not considered to be financially feasible. The Biden plan was scrapped during negotiations over what became the Inflation Reduction Act.

A correction was made on

Oct. 8, 2024

:

An earlier version of this article, in one reference, misspelled the surname of a health policy professor at Harvard who studies long-term care. He is David Grabowski, not Grabowksi.

When we learn of a mistake, we acknowledge it with a correction. If you spot an error, please let us know at nytnews@nytimes.com.Learn more