As the No. 6 subway train creaked toward an elevated Bronx station on Tuesday, one of Representative Alexandria Ocasio-Cortez’s constituents stood across the street, struggling to understand his congresswoman’s opposition to the most sweeping public works legislation in generations.

The infrastructure bill, which passed the House last week, offers New York billions of dollars, and it was a top priority for President Biden, congressional Democrats and even 13 Republicans — four of them from New York.

Yet Ms. Ocasio-Cortez and five fellow progressives voted against it; they argued that the bill was too modest and sought to use their votes to pressure wavering moderates to support a bigger climate and social safety net bill that is pending.

“Right mind-set,” said Emmet Allen, 27, the constituent who stood outside the Buhre Avenue station in Pelham Bay. “But wrong execution.”

For more than three years, Ms. Ocasio-Cortez has helped alter the fabric of the Democratic Party. After defeating the powerful incumbent Joseph Crowley in 2018, she instantly became the face of an ascendant ideological movement that racked up electoral victories, pushed party leaders leftward and electrified many younger voters, even as she has withstood a torrent of right-wing abuse that showed itself again this week.

She remains overwhelmingly popular among many in her district, who watched her rocket from working as a waitress and bartender to becoming one of the Democratic Party’s biggest stars.

But where Ms. Ocasio-Cortez was once seen by many political observers as at the vanguard of the party’s new direction, she may now be more emblematic of its divides.

Even in her New York City district — perceived as one of the most liberal in the nation — there are sharp disagreements unfolding over how far left the party should go and how change is best achieved, according to interviews with more than three dozen constituents, elected officials and party leaders.

At no time has that been clearer than over the last week, as New Yorkers debated her approach to the bipartisan infrastructure measure that will fund much-needed improvements to subways, roads, bridges and sewers, despite falling short of initial Democratic hopes.

Simultaneously, Democrats are battling over how to rebound from recent electoral defeats around the country and in New York, where Republicans seized Democratic seats in bedroom communities like Nassau County and even, apparently, in a local race that includes a slice of Ms. Ocasio-Cortez’s district.

As Ms. Ocasio-Cortez explained her infrastructure position over Instagram and headed to Glasgow for an international climate summit, her constituents, from the bustling, heavily Spanish-speaking neighborhood of Corona, Queens, to placid blocks of Pelham Bay, grappled with her approach.

To some, including those who admire her, the question seemed to boil down to this: Is serving in government about pushing boundaries on urgent issues like climate and structural inequality? Or is it more about getting tangible results for riders aboard the No. 6 train?

“She is saying she is voting for her constituents,” said Jennifer Shannon, 51, who helps run a civic group in College Point, Queens, and who has voted for Ms. Ocasio-Cortez. “I’m not saying they don’t all care about the environment, but I think people in her district are tired of the conditions of our streets and our subways.”

This was not the first time that Ms. Ocasio-Cortez has bucked her party to oppose a bill that did not, in her view, go far enough. She was the only Democrat to oppose a $484 billion coronavirus relief package that she felt was inadequate for her district, which was devastated by the virus in the spring of 2020. But she has also worked closely with party leadership at other times — for example, helping to secure federal funding to assist with funeral costs for Covid-19 victims.

There was only scattered criticism of Ms. Ocasio-Cortez’s opposition to the infrastructure bill from Democrats in Washington. With more than enough projected Republican votes for passage, Democratic leaders knew the congresswoman could vent her frustration without endangering the bill, according to congressional aides familiar with discussions among progressives.

Ms. Ocasio-Cortez, who was not made available for an interview, and her allies argue that her vote was driven precisely by her sense that more is needed to improve lives for historically underserved constituencies and to capitalize on what may be a fleeting window of opportunity for Democratic clout in Washington.

“All I’ve heard across the district has been support for the decision that she made,” said Assemblyman Zohran Kwame Mamdani, a democratic socialist who represents one of the most left-leaning neighborhoods in the district. “A lot of that is based on the fact that she was elected on the promise of fighting for more than the crumbs we’ve been told to accept.”

In a 71-minute Instagram video viewed more than 700,000 times, Ms. Ocasio-Cortez seemed aware that some constituents would be unhappy.

By turns righteous, disappointed and vulnerable, she said her stance was predicated on two concerns: the potential that the bill would increase planet-warming emissions with giveaways to fossil fuel companies; and the need for leverage to push for companion legislation that many Democrats hope will generously fund additional climate solutions and housing assistance and protect undocumented immigrants.

“If I have to choose between my political image or whatever, and staying true to my community,” she said, “I’m going to do what my district asks of me every time.”

When she is in her district, no one is a bigger political star, and few in New York politics can draw more focus to local issues.

Sadye Paez, 43, of Corona, said she appreciated the congresswoman’s approach to the infrastructure debate. “It’s a way of bringing attention to these communities,” she said.

Through social media, many voters also feel personally connected to Ms. Ocasio-Cortez, who intersperses wellness tips and pictures of her dog, Deco, with discussions of policy and procedure.

But some constituents, business leaders and elected officials say that day to day, she is not always accessible.

“Ideology sometimes has to go out the window when it comes to bringing home the bacon,” said Thomas J. Grech, the chief executive of the Queens Chamber of Commerce, who said he has never been able to successfully schedule a meeting with the congresswoman, as he does with her peers.

At around 3:30 p.m. Tuesday, Ms. Ocasio-Cortez’s Queens district office was bolted shut, and what appeared to be a window on the door was blacked out. When Jahangir Hossein, a cabdriver, tried to drop off paperwork, he was informed over a halting intercom system that her team was working remotely, and that he should return on Wednesday.

The scene stood in contrast to one unfolding down the hall, as New Yorkers walked in and out of State Senator Jessica Ramos’s office.

Lauren Hitt, a spokeswoman for Ms. Ocasio-Cortez, said the congresswoman’s district offices were generally open on Mondays and Wednesdays. They intend to move to in-person staffing four days a week in January, public health trends allowing, with a commitment to returning to five days a week. In the meantime, their processing of casework has accelerated, her team said.

“The pandemic definitely forced us to adjust our in-office presence, but we are still serving our constituents,” Ms. Hitt said.

She pointed to a range of creative efforts focused on meaningful constituent services, from food distributions, to starting a tutoring program to assist with remote learning, to canvassing neighborhoods after Hurricane Ida to encourage residents to apply for federal assistance.

Still, State Senator John C. Liu of Queens said there was a distinction between the congresswoman’s perceived presence and that of many of her colleagues — a dynamic, he suggested, that cuts two ways.

“She’s known in the district largely like she’s known internationally, which is, she’s a celebrity,” he said. “The fact that she has such a large platform inures to the benefit of her constituents, even if they can’t see her in person much of the time.”

He suggested that her visibility in the district — ubiquitous online, less so in person — stood in contrast to “most of the other Congress members in New York.”

Ms. Hitt noted that in 2020, Ms. Ocasio-Cortez easily defeated well-funded challengers who “ran heavily on the idea that she was a celebrity not present in the district.”

She remains formidable this year, with no apparent primary challenger yet, and almost $6 million in her campaign account.

Yet the Democratic Party’s unexpectedly steep losses on Election Day have rekindled a longstanding debate over how to motivate portions of the base without alienating voters in the middle, one that is playing out even on Ms. Ocasio-Cortez’s turf, if not in her own race.

Despite the 14th District’s overall leftward bent — the Democratic Socialists of America have had some of their greatest city successes in western Queens and remain powerful — the relatively moderate New York City mayor-elect, Eric Adams, won other swaths of the district in his primary, while in the general election, Republicans made inroads in some pockets.

“I stood in front of a poll in my community all day and I heard it over and over: ‘Oh, the Democrats are terrible. The Democrats are not helpful, they fight among themselves, they don’t care about us, they are socialists,’” said Tony Avella, a moderate Democrat who appears to have lost a City Council district in Queens that includes a more moderate part of Ms. Ocasio-Cortez’s congressional district.

“It’s a warning,” he added, referring to Ms. Ocasio-Cortez as a “lightning rod” in the community.

But John Samuelsen, the international president of the Transport Workers Union, which represents Metropolitan Transportation Authority workers, said moderate Democrats like Mr. Avella had it backward. Democrats could avoid more drubbings, he argued, by embracing the kind of economic populism espoused by Ms. Ocasio-Cortez.

A desire for enhanced health care coverage, paid family leave and well-paid jobs is “what all Americans have in common,” Mr. Samuelsen argued.

Some of the most vigorous debates around Ms. Ocasio-Cortez’s vote, and her politics more broadly, have played out in local online groups.

Jack McCleland, a retired Brooklyn Public Library employee, was so frustrated when he read about the “no” vote on infrastructure that he fired a grenade into a Facebook group designated for his Jackson Heights, Queens, neighborhood.

“AOC voted against the Infrastructure Bill,” he wrote. “Time for her to go.” It spawned 145 comments.

In an interview, Mr. McCleland, 74, said he considered himself a devoted Democrat who wants ambitious climate and health legislation. But he said he now worried that in her attempts to push the party to the left, Ms. Ocasio-Cortez was undermining its ability to govern.

“We have to get something done, otherwise we are going to be the party of ‘no’ and we are not going to save the House or Senate,” he said, adding that he thought Ms. Ocasio-Cortez was “grandstanding.”

Browne Smith, a former ballet dancer and actor, jumped in to plead with her neighbors to listen to the congresswoman.

“It’s called a protest vote,” she said in an interview, arguing that Ms. Ocasio-Cortez’s actions had highlighted what remained unfinished in Mr. Biden’s agenda without risking the passage of the infrastructure bill, given its Republican support.

“I support her speaking out and voting against things that get people talking about injustices that need to be fixed,” she said. “Maybe she is still learning the games of politics because she’s young. But she’s damn good at it.”

Sean Piccoli and Precious Fondren contributed reporting.