As Gov. Kathy Hochul of New York prepares to deliver her State of the State address on Tuesday, her priorities seem firmly focused on the voter frustrations that fueled Donald J. Trump’s election to the presidency in November.

Over the last month, Ms. Hochul has announced proposals to cut taxes for parents, make school lunch free and give millions of New Yorkers rebates of up to $500 depending on their income. These ideas have all been packaged as part of an “affordability agenda.”

And on Tuesday, Ms. Hochul is expected to announce a new series of middle-class tax cuts, and devote a portion of her speech to efforts to combat crime and mental illness.

“You tell us you need help; we hear you need help,” Ms. Hochul said earlier this month when previewing some of the proposals that will be included in her speech and her executive budget, which will come out next week. “We’re going to continue delivering real solutions that make a difference.”

Ms. Hochul, a centrist Democrat, is also expected to reinforce the notion that New York will protect vulnerable groups from aggressive policies adopted by the incoming Trump administration, especially concerning recent immigrants, according to someone familiar with her planned speech.

The governor, however, has no plans to adopt the kind of “resistance” fervor that characterized responses to Mr. Trump’s first inauguration in 2017, the person said.

Ms. Hochul’s reticence may reflect the precariousness of her own political future. Her popularity has plummeted in recent years, and rivals from both parties appear to be preparing to challenge her in 2026.

One potential Republican candidate, U.S. Representative Mike Lawler, who represents parts of the Hudson Valley, will be in Albany on Tuesday to offer his party’s rebuttal to her remarks, alongside Republicans from the State Legislature.

Mr. Lawler has bashed the governor on congestion pricing, crime and a litany of other issues, and is certain to do the same on Tuesday.

Last month, Siena College released a poll that found that just 33 percent of voters wanted Ms. Hochul re-elected and about 39 percent had a favorable view of her. The poll also showed that about 43 percent of New York voters think lowering the cost of living should be the Legislature’s top priority this year. Creating more affordable housing was also high on the list of priorities.

Ms. Hochul has seemed to tailor some of her State of the State proposals to those voter concerns. Her proposed “inflation refund” program would route roughly $3 billion in excess sales tax revenue directly to New Yorkers.

And Ms. Hochul’s proposed expansion of the state’s child tax credit would more than double what some families currently receive. In recent years, New York’s poorest families have typically received up to $330 per child. If the plan were enacted, eligible families could get tax credits of up to $1,000 per child under the age of 4. Families with children ages 4 to 16 could get credits of up to $500 per child.

These proposed tax cuts and refunds come as the state contemplates how to plug a multibillion-dollar funding hole for infrastructure improvements to public transit. Last month, Carl E. Heastie, the Assembly speaker, and Andrea Stewart-Cousins, the Senate majority leader, rejected the Metropolitan Transportation Authority’s capital proposal, citing in part the plan’s $33 billion deficit.

“Everything will have to be on the table,” Ms. Stewart-Cousins said when asked on Monday if new taxes to fund regional transit were under consideration.

Crime continues to be another pressing concern for New York voters, especially in the New York City subway, where a number of violent incidents have drawn attention to rider safety. Ms. Hochul is expected to use her speech to propose adding more lights and barriers on platforms, along with deploying more law enforcement officers on trains.

She is also expected to elaborate on her efforts to loosen the standards for involuntary commitment and expand laws relating to court-ordered assisted outpatient treatment for people with mental illness. Mayor Eric Adams of New York City has been a major proponent of these changes, saying they will go a long way toward addressing some of the perceived disorder on the trains and will help vulnerable people.

Brian Stettin, Mr. Adams’s senior adviser on severe mental illness, said in an interview that Ms. Hochul’s public comments had been encouraging and showed an urgency about the problems that outreach workers and others were confronting.

“Her comments have been consistent with what’s in our package,” he said. “But we are waiting to see the details.”

The governor will also propose spending $400 million to breathe new life into Albany’s struggling downtown, including $150 million for the aging New York State Museum. The proposed funds for the state’s capital were earlier reported by The Albany Times Union.

Jay Root contributed reporting.

The labor union representing stagehands went on strike Sunday against Atlantic Theater Company in Manhattan, prompting the prestigious nonprofit to postpone two productions that had already begun performances and to warn that union demands could force the closing of the Atlantic and other Off Broadway nonprofits.

Both the International Alliance of Theatrical Stage Employees, the labor union, and the Atlantic said negotiations had broken down, but each side blamed the other for the stalemate. The strike comes at a time when many nonprofit theaters around the country are running deficits and facing serious financial challenges, but also at a time when the labor movement nationally has been emboldened and insistent on better pay and working conditions. Actors’ Equity, the labor union representing stage performers, said it supported the stagehands.

The Atlantic canceled Sunday matinee and evening performances of two new plays, “Grief Camp” and “I’m Assuming You Know David Greenspan,” both of which began previews last week. The Atlantic said Sunday the productions would be postponed indefinitely.

The dispute has broad ramifications for Off Broadway nonprofits, which have for decades nurtured many of the nation’s most acclaimed theater artists and shows. Off Broadway crew members have not traditionally been unionized, but the International Alliance of Theatrical Stage Employees has been working on organizing them, and the Atlantic’s crew voted last February to join the union.

The Atlantic was founded in 1985 and operates two venues in Chelsea. The company has staged more than 200 productions, including three musicals that went on to win the best musical Tony Award after transferring to Broadway: “Spring Awakening,” “The Band’s Visit” and “Kimberly Akimbo.” Another musical first staged at the Atlantic, “Buena Vista Social Club,” is scheduled to begin performances on Broadway next month. The company had an annual budget of $15 million in fiscal 2023, according to a filing with the Internal Revenue Service.

The union, in a statement, accused the Atlantic of stalling negotiations on their first contract and said it had filed unfair labor practice complaints against the company with the National Labor Relations Board, accusing the company of failing to negotiate in good faith.

“Atlantic Theater’s refusal to bargain fairly has left the crew no choice but to strike,” the union’s international president, Matthew D. Loeb, said in the statement. “We are prepared to resume negotiations as soon as Atlantic Theater is ready to bargain in good faith.”

The theater issued its own statement, describing itself as “pro-union” and saying it had made generous offers, but warning that the union’s demands could weaken Off Broadway institutions.

“We have offered a good faith agreement with nearly a 20% increase in wages and other benefits,” the company said.

The company also said, “Most of Off Broadway is facing a precarious financial situation, running significant deficits since returning from Covid. If IATSE is successful in getting their proposed financials with Atlantic, it would set a precedent for other Off Broadway companies and we may see the demise of some of our greatest institutions, including Atlantic.”

The Actors’ Equity assistant executive director, Calandra Hackney, issued a statement of support for the stagehands, saying “Actors’ Equity Association stands in solidarity with these workers,” and adding, “We have full faith that IATSE is negotiating terms that are fair and appropriate for their members, and we look forward to the shows resuming when an agreement has been reached.”

Brad Lander, the New York City comptroller who is running for mayor, will unveil his signature campaign issue on Monday: trying to end homelessness on the streets and subways for people with severe mental illness.

The problem has vexed leaders in many large cities, but perhaps none more so than in New York, where a recent series of violent attacks on the subway has rekindled safety concerns and heightened calls for law enforcement and the courts to do more to keep troubled people off the streets.

Mr. Lander’s 75-page-plus plan calls for expanding subway outreach teams and embracing a “housing first” model that has been successful in other cities, including Houston and Denver. Mr. Lander would focus on roughly 2,000 homeless people with serious mental illness and place them in vacant apartments known as single-room-occupancy units, or S.R.O.s.

“New Yorkers are stressed out about lack of safety on the subway and our streets, and a huge amount of that is mentally ill homeless folks who, in some cases, become a real danger, as we’ve seen in recent weeks,” he said. “We dug in and realized this is a solvable problem.”

Mr. Lander said he believed he could get most or all homeless people with serious mental illness off the streets and into some form of supportive housing in his first two years as mayor. The plan would cost about $100 million in the first year, and roughly $30 million per year thereafter, with about half going toward renovating vacant single-occupancy apartments that would provide an array of on-site services.

The number of people living in the streets and subways of New York City was estimated at 4,140 last year — the highest level in nearly two decades. Rents have soared, and roughly one in eight public school students is homeless.

Those factors have helped make mental health and homelessness major issues in the mayoral race — with more attention focused on the problems after a woman was lit on fire and killed on a train, and subway riders have been pushed onto the tracks by people with mental illness.

Moving some of the city’s most fragile and least stable residents into permanent housing and having them stay requires a herculean level of coordination among multiple stakeholders. They include hospitals; jails; the criminal justice system; nonprofits that offer street medical services and provide housing; and city and state social service agencies and health authorities.

That has not stopped city leaders from trying to navigate that patchwork of bureaucracies.

Last week, during his fourth State of the City speech, Mayor Eric Adams announced a $650 million plan to address street homelessness that includes building new housing for people with serious mental illness and adding 900 “safe haven” beds, which are temporary housing options that offer more privacy and fewer restrictions than typical shelters.

Kayla Mamelak Altus, a spokeswoman for Mr. Adams, said in a statement that the mayor had “rejected the notion that leaving people to sleep on the street was acceptable” and helped move 8,000 New Yorkers from the subways into shelters, among other efforts. She said there was “still more work to be done,” pointing to the plan that the mayor just unveiled.

“It’s hard to imagine a fraction of this being achieved under Brad Lander, who would prefer to see our streets littered with encampments and our most vulnerable rotting away in filth,” she said.

Other mayoral candidates have pledged to address homelessness, including Jessica Ramos, a state senator from Queens who released a mental health plan last week. Ms. Ramos proposed building 20 community centers that offer therapy and filling vacant supportive housing units.

“As mayor, I will declare a mental health emergency on Day 1 of my administration so we can deliver services to suffering New Yorkers swiftly and effectively,” Ms. Ramos said.

Scott Stringer, a former comptroller, said in a statement that he would remove people who pose a danger to themselves or others and would expand mental health outreach teams. He said that New Yorkers felt “abandoned by city government.”

Zellnor Myrie, a state senator from Brooklyn, said the Adams administration was “letting too many people who are demonstrating behavioral disturbance fall through the cracks because of a byzantine network of programs and systems.” He said he would expand outreach teams and housing.

The issue has long bedeviled mayors. Bill de Blasio announced a $100 million plan to “end long-term street homelessness” in five years. After eight years as mayor, Mr. de Blasio acknowledged that the issue was his greatest disappointment.

Mr. Lander wants to rely on the “housing first” model that has allowed Houston to move more than 25,000 homeless people into apartments and houses. The approach moves the most vulnerable people straight from the streets into apartments, not into shelters, and does not require them to first wean themselves off drugs, complete a 12-step program or get a job. Evidence shows that the strategy keeps people housed, but it is unclear if it saves money or leads to better health outcomes.

New York City has about 40,000 supportive housing units, and most of their occupants moved there from shelters or other temporary housing. Mr. Adams’s administration started a “housing first” pilot program in 2022 that planned to reach 80 adults living on the street. Mr. Lander wants to significantly expand the program.

Mr. Lander’s plan would also create a centralized database for all mental health crisis responses to help prevent people from falling through the cracks.

Steven Banks, the city’s social services commissioner under Mr. de Blasio, said that Mr. Lander’s plan was “on the right track” based on his experience in city government and his decades at the Legal Aid Society, the main legal provider for poor New Yorkers.

The plan argues that Mr. Adams has failed to adequately address the city’s mental health crisis. It found that the mayor’s broad sweeps of homeless encampments had connected only three people with permanent housing during a period in 2022, and that his administration had not made enough progress on promises to create 360 therapeutic beds for people in jails and to create 15,000 units of supportive housing that include social services.

It also cited a lack of coordination among the various city agencies responsible for caring for those with mental health issues, including hospitals, outpatient treatment teams and homeless shelters — failures highlighted in a 2023 investigation by The New York Times.

Mr. Lander also seeks changes in the rules regarding involuntary hospitalization of people in psychiatric crisis, which are set by the state. Gov. Kathy Hochul said recently that she would push to loosen the standards for involuntary commitment.

Mr. Lander wants hospitals to consider a patient’s history when deciding whether to admit them and to allow nurses to be able to evaluate individuals for involuntary hospitalization, among other changes.

Mr. Adams, a former police officer who ran for mayor on a public safety platform, has taken a tough stance on clearing the streets of homeless people, but data shows that the population has grown. In January 2022, just after Mr. Adams took office, the city estimated that there were about 3,400 people living in streets and subways.

Another measure of street and subway homelessness is the number of unsheltered people on the caseload of outreach workers. That, too, has gone up under Mr. Adams, to about 3,250 in June 2024, from about 2,050 in June 2021.

Mr. Lander, when asked how he could fix the problem when so many other elected officials have struggled, cited his experience leading a housing nonprofit and his singular focus on the issue. He said he would ask his staff for weekly updates on the city’s “by name list” of people who are homeless to make sure they were on a path to housing.

“I’m making this my No. 1 promise to New Yorkers, and it will be my No. 1 focus when I become mayor,” he said.

Jan Ransom and Amy Julia Harris contributed reporting.