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.