ALBANY — Gov. Andrew M. Cuomo, delivering his State of the State address along with a budget proposal heavy on infrastructure, laid out an ambitious social agenda on Wednesday that focuses on problems not so easily solved with cash: the erosion of confidence in the criminal justice system, public schools and teachers that he said were failing students, and a creeping sense that economic mobility is not what it once was.
Though these are national problems, Mr. Cuomo argued, New York State must take the lead in solving them.
“The young girl who sleeps in a homeless shelter tonight is our daughter,” he said. “The farmer in the Southern Tier who is struggling to make ends meet, that farmer is our brother. The child who lives in poverty in Rochester today is our child.”
Much of what Mr. Cuomo is proposing will encounter stiff resistance in the divided Legislature, where Republicans are now firmly in control of the State Senate, and Democrats dominate the State Assembly.
The most bitter fight in Albany could come on education reform. Though Mr. Cuomo, a Democrat, offered up $1.1 billion in new school aid, he attached strings that could kill the deal for allies of the teachers’ unions in the Assembly: a much more rigorous teacher evaluation system to replace the current one, new hurdles for teachers on the path to tenure, and an expansion by 100 of the limit on the number of charter schools statewide.
“Don’t ask the taxpayers of New York to throw good money after bad,” he said. “We’ve done that for decades. Let’s make the hard choices once.”
He also called for new measures to heal widening police and community rifts in the aftermath of the events in Ferguson, Mo., and on Staten Island last year: allowing district attorneys to shed light on the grand-jury process when police officers are investigated but not indicted in fatalities, and promising to appoint independent monitors to review such cases. Mr. Cuomo also offered to pay for better protections for police officers, like bulletproof glass and vests.
Over all, the governor’s spending plan totals $150 billion, an increase of 4.9 percent compared with the current year. The increase in state operating funds would be limited to 1.7 percent.
Beginning with his inauguration in early January, Mr. Cuomo has undergone a rhetorical transformation of sorts, from the first-term fiscal hawk and corrective agent facing down Albany’s dysfunction to a champion of liberal causes, like addressing income inequality.
Affirming his call to raise the minimum wage, currently $8.75, to $11.50 in New York City and $10.50 in the rest of the state, Mr. Cuomo drew applause that seemed to grow more enthusiastic the deeper he went into daunting social problems, like economic stagnation upstate, poverty and homelessness.
Mr. Cuomo’s 84-minute speech, delivered in a convention center adjacent to the Capitol, was meant to set the tone for the new legislative session and for the governor’s second term. His proposals and budget, which combined both his fondness for practical solutions and his knowledge of Albany deal making, were detailed in a written briefing book that ran more than 500 pages.
But his paired inducements to both sides in the education reform debate, and to critics and defenders of the police alike, did not immediately win anyone over.
On education, his offer of increased state funding was counterbalanced by measures including one to solidify the teacher evaluation system; fewer than 1 percent of teachers were found to be ineffective under the current one. Calling the status quo “baloney,” he proposed increasing the weight of students’ test scores in the new ratings.
He also proposed to require teachers to earn five straight years of high marks before gaining tenure. The probation period now is three, although districts can extend it, and state law says a teacher’s rating must be a “significant factor” in employment decisions, without explaining what that means.
Mr. Cuomo also proposed raising the limit on the number of charter schools allowed in the state to 560, from 460, and increasing the amount of funding those schools receive. There are 248 charter schools operating in the state; they are privately run but publicly funded and are frequently nonunionized.
But the Assembly speaker, Sheldon Silver, a Democrat, said he was not sure it was “urgent” to increase the cap on the number of charters, since there was still room to open some charters under the current cap. And the leaders of the state’s teachers’ unions immediately condemned the governor’s proposals, as did the president of the New York State A.F.L.-C.I.O., Mario Cilento.
Mr. Cuomo’s budget also included legislation, known as the Dream Act, that would expand state tuition assistance to undocumented immigrants, as well as an education tax credit for individuals and corporations, which many Democrats oppose. The two measures will be linked, forcing lawmakers to take both or none, the administration warned.
Immigrant advocacy groups celebrated the Dream Act’s inclusion; the bill borrows its name from failed federal legislation that would have provided a path to citizenship for immigrants who were brought to the country illegally as children.
But Dean G. Skelos, a Republican who is the Senate majority leader, was quick on Wednesday to throw up a formidable roadblock. “I think we’ve made it very clear that the Dream Act is a no-go,” he said.
For his part, Mr. Silver said the tax credit proposal would go nowhere. “I support giving parents relief from the costs of education, but I’m not sure that providing corporate tax relief is the way to provide the relief to parents who need it,” he said.
Mr. Cuomo’s seven-point agenda on criminal justice could be nearly as contentious.
He proposed giving district attorneys the latitude to release information about a grand jury’s collective thinking when it declines to hand down an indictment of a police officer investigated over a fatality. “So people can know what actually happened,” the governor said.
Mr. Cuomo said he would name an independent monitor in fatal episodes involving the police and civilians, with the power to review grand jury deliberations and recommend special prosecutors.
Along with bulletproof vests and patrol car windows to protect officers, and body cameras to record incidents, the governor said his agenda would go a long way to restoring trust and respect between the police and the community.
But some details remained elusive on Wednesday, even to those who praised the idea, with several also suggesting that the governor had not gone far enough. “Real police accountability is still so painfully lacking,” said Priscilla Gonzalez, organizing director of Communities United for Police Reform. “Cuomo must do more to help our communities achieve it.”
Police unions, meanwhile, said new equipment would do nothing to allay their concerns about the scapegoating of officers. “I reject the concept that those tools be horse-traded for criminal justice reforms designed to disrupt the due process rights of law enforcement,” said Michael J. Palladino, president of the Detectives’ Endowment Association.
Mayor Bill de Blasio of New York City said the governor’s focus on increasing wages, expanding prekindergarten and criminal justice was heartening, up to a point. “I think it’s good to see them front and center in the agenda,” he said. But, he added, “I think we’re all going to be judged by what we achieve.”
Mr. Cuomo spoke warmly of his father, former Gov. Mario M. Cuomo, whose death on Jan. 1, hours after Mr. Cuomo’s ceremonial swearing-in, caused the State of the State speech to be rescheduled.
And Mr. Cuomo ended his speech with almost the exact words his father had uttered to end his first inaugural address in 1983: “For all the ceremony, and the big house, and all the pomp and circumstance, please don’t let me forget what makes New York New York,” he said.
Reporting was contributed by Thomas Kaplan and Kate Taylor from Albany, and Al Baker, Mireya Navarro and Kirk Semple from New York.
A version of this article appears in print on January 22, 2015, on page A1 of the New York edition with the headline: Cuomo Recasts Social Agenda for a New Term. Order Reprints| Today's Paper|Subscribe