Gov. Kathy Hochul of New York proposed slashing the state’s income tax for most residents as part of a sweeping populist agenda that she planned to outline in her State of the State address on Tuesday.

The speech revolved around a series of proposals, which Ms. Hochul has called her “affordability agenda,” designed to court struggling New Yorkers who voiced their frustration in November and weakened the Democratic Party’s grip on the state.

The tax cut, according to a briefing book released in advance of her speech, would be given to those who earn up to $323,000 per year for joint filers, or 77 percent of the state’s taxpayers. The move would “deliver over $1 billion in tax relief to more than 8.3 million taxpayers,” according to the briefing material.

Ms. Hochul also intends to cut taxes for parents, make school lunch free and give millions of New Yorkers rebates of up to $500 depending on their income.

It was not immediately apparent how many of these proposed programs would be enacted or funded. But it was clear that the re-election of Donald J. Trump had been on her mind as she crafted the address.

She highlighted proposals to protect the identities of doctors who prescribe anti-abortion drugs and add more state troopers to patrol the northern border. Expectant mothers would also qualify for a $100 monthly benefit during pregnancy; mothers on public assistance would receive an additional $1,200 when their child is born.

The governor, however, seemed to shy away from adopting the kind of “resistance” fervor that characterized responses to Mr. Trump’s first inauguration in 2017.

Ms. Hochul’s reluctance to do so, combined with her push on affordability, 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, Representative Mike Lawler, who represents parts of the Hudson Valley, stood alongside Republicans from the State Legislature Tuesday morning and criticized the governor on a litany of issues, including congestion pricing, which he said only put more financial strain on New York commuters.

“She is a feckless and failed governor who needs to be replaced in 2026,” Mr. Lawler said, later adding that her speech on Tuesday “isn’t about working across the aisle to make New York a better, more affordable, safer place to live.”

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 thought 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.

Before the speech, the Erie County executive, Mark C. Poloncarz, applauded Ms. Hochul’s focus on bread-and-butter issues but said she would have to keep promoting her agenda beyond the State of the State address for it to sink in.

“One of the things that you can’t do is make these big announcements, and then that’s it,” he said. “People want to see and know their elected officials. They want to know more than you’re just investing in affordability issues, but that you understand their issues in their communities.”

Mr. Poloncarz, a Democrat, added that the governor needed to remind people that “the Democratic Party is the party of the working class. We’re the ones that brought Social Security, we’re the ones who came up with Medicare. We’re the ones of the Affordable Care Act, which the prior administration tried to eliminate.”

The 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.

Ms. Hochul said in papers accompanying the speech that she wants “a balanced mix of federal, state, city and M.T.A. contributions in line with historical practice, alongside new revenue sources to be agreed during budget negotiations this spring and cost efficiencies to be achieved by the M.T.A.”

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 wants to fund more lights and barriers on platforms, along with deploying more law enforcement officers on trains. She also wants to tweak and streamline how the discovery process works in preparation for trials.

And she is 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 and Maya King contributed reporting.

Gov. Kathy Hochul of New York on Monday announced her intention to limit access to cellphones in schools for students in kindergarten through 12th grade as part of her latest push to address children’s reliance on the devices.

In a statement, which provided no other details, the governor said she would include the legislation in her proposal for next fiscal year’s budget. She billed the initiative as a follow-up to one of her key achievements last year, the passage of legislation designed to protect young people from addictive algorithms on social media. She cited a Pew Research poll that showed 72 percent of high school teachers described students being distracted by cellphones as a “major problem.”

“Young people succeed in the classroom when they’re learning and growing — not clicking and scrolling,” Governor Hochul said Monday. “My upcoming budget proposal will put forth a new statewide standard for distraction-free learning in schools across our state.”

Speaking to high school and college students at Hudson Valley Community College on Monday, the governor acknowledged that restricting cellphone use might make her “very unpopular.”

Los Angeles Unified became the largest school district in the United States to ban cellphones last year. Virginia, Ohio and Minnesota are among the states that have moved to crack down on the devices in schools.

In New York City, Mayor Eric Adams backed away from a plan to ban cellphones in schools in August, saying the city wasn’t “there yet.”

In September, New York State United Teachers, the state teachers’ union, called for a “bell-to-bell” policy that would restrict cellphone use from first period to dismissal. The union’s president, Melinda Person, has said that the union was working closely with the governor to craft a plan.

But the idea has its detractors as well. Some New York parents who were students during the Sept. 11 terrorist attacks have expressed reservations about losing the ability to contact their children in an emergency. Principals have questioned who would foot the bill for equipment to collect phones. And some teachers have wondered how they would be expected to discipline students who broke the rules.

In a statement on Monday, a spokeswoman for the United Federation of Teachers, New York City’s teachers’ union, said that the organization supported state and city restrictions on cellphones in public schools, as long as a number of conditions were met.

The union said teachers should not be responsible for enforcing the restrictions; school districts should shoulder the cost instead of individual schools; enforcement should be consistent from student to student; and schools should have emergency contact lines set up for parents.

Many of New York City’s more than 1,500 public schools already restrict cellphone use. Some middle schools require children to place their phones in cubbies along the walls of their classrooms. Many high schools hand out locked fabric pouches for phones that students carry in their bags throughout the school day.

Brad Hoylman-Sigal, a state senator who represents a large swath of the West Side of Manhattan, introduced a bill last week that would prohibit students from accessing their phones on school property. He said he saw his bill as a starting point for a conversation in the State Senate.

He said he hoped that the governor’s plan would include a way for students to safely and securely hand over their phones and then get them back at the end of the day.

“As a parent of a 14-year-old daughter, I understand how phones are an obstacle in the learning environment,” Senator Hoylman-Sigal said. “At the same time, I appreciate that parents want their children to have phones when they’re on the subway or on a bus. So I hope the governor’s proposal embraces both of those needs.”

Speaking at the community college on Monday, Governor Hochul described hearing from students who told her about how they struggled to put away their phones because they are feared they would “miss something.”

“There’s so much pressure on all of you, and I’ve got to help you with that,” she told the students. “That’s my job.”

Troy Closson and Benjamin Oreskes 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.”