“That sounds expensive,” Ms. Nixon said. “You know what? It is, and it should be. We can do it by requiring that millionaires, and billionaires and corporations, who this economy has blessed, pay their fair share for all of our children.”

If she were elected, Ms. Nixon’s tax plan would likely face obstacles in Albany. The New York Senate, currently controlled by Republicans, has opposed raising taxes. And some Senate Democrats have also cautioned against tax increases, should they win control over the chamber in November.

A Siena College poll released Wednesday found Ms. Nixon trailing her primary opponent, incumbent Gov. Andrew Cuomo, 26% to 61%. That is down from 27% to 58% in April.

Ms. Nixon, a public-school advocate and actress, has been running a campaign to the left of Mr. Cuomo, challenging his record on issues like mass transit and criminal justice. She has painted Mr. Cuomo as an ally of big businesses and wealthy residents at the expense of students, particularly black and Latino children in high-poverty schools.

“The fact is this state spends more money per pupil than any state in the United States of America,” Mr. Cuomo said at news conference Wednesday. “And no state has done what we’ve done. Not in terms of funding, not in terms of free college, not in terms of security.”

A spokeswoman for the governor said school spending has increased by 36% since 2012 and will hit a record $26.7 billion during the 2018-19 school year.

New York spent $22,366 per pupil in 2016, nearly double the national figure, according to the U.S. Census Bureau.

Ms. Nixon’s education plan calls for relaxing certain requirements to qualify for Excelsior Scholarships, a program championed by Mr. Cuomo that pays for tuition for some students in the State University of New York and City University of New York systems.

She also wants to provide prekindergarten for every low-income 4-year-old in the state and for all 4-year-olds in high-need districts. The current budget calls for an additional $15 million for prekindergarten; Ms. Nixon wants an additional $361 million for these programs.

Ms Nixon promised to boost a major source of K-12 funding called “Foundation Aid” by $4.2 billion, phased in over three years.

Foundation Aid is intended to send extra dollars to districts with high numbers of children who are poor, disabled and English-language learners, but the formula dates back to 2007 and many districts complain it hasn’t been fully funded since the recession hit. Many education experts say the formula is flawed.

Ms. Nixon said she would fully fund Foundation Aid and appoint a commission to update it.

Rick Timbs, executive director of the Statewide School Finance Consortium, which seeks fair distribution of school aid, said there isn’t a simple solution for Foundation Aid. “While the overarching goal she has may sound important and helpful, the key thing is the detail on how distribution would actually occur,” he said.

To pay for her education plan, Ms. Nixon wants to raise state-tax revenues by $8.7 billion annually. She said some $5.5 billion would come from income-tax increases, and $3.2 billion would be generated from corporate-income tax increases and other changes to taxes on large businesses.

The income tax increases would begin at $300,000 for married couples filing jointly. Their rates would rise from 6.85% to 7.35% under the plan. The top tax rate would jump from 8.82% to 10.25% for couples making $10 million or more.

E.J. McMahon, adjunct fellow at the Manhattan Institute, a right-leaning group, challenged the idea that taxpayers and business would be willing to pay more. He said wealthy New Yorkers are already paying higher taxes due to recent federal tax changes, which put a $10,000 annual cap on state and local tax deductions.

Her tax plan is “completely unrealistic and excessive,” Mr. McMahon said, adding that it is “based on the assumption that businesses and individuals alike are simply oblivious to higher tax rates.”

Jonas Shaende, chief economist at the left-leaning Fiscal Policy Institute, said he supported efforts to find more revenues through taxes on the wealthiest residents. While some critics of boosting taxes say high-earners would flee New York to escape increases, Mr. Shaende said many aren’t as mobile as they might seem. “There has to be a lot more happening on top of the tax situation to make them leave,” Mr. Shaende said.

Cuomo supporters also questioned whether Ms. Nixon’s tax plan would produce enough money to pay for her education program and fix the New York City subways—both of which she pledged to pay for with higher income taxes.

A spokeswoman for the Nixon campaign said her tax plan would produce $1.4 billion more than is needed to pay for her education programs. Most of that remaining pot will go toward upgrading the city’s subways, she said.

Ms. Nixon also wants to pay for subway fixes with a polluters tax on businesses and congestion pricing for drivers. That could raise an additional $8.5 billion, the spokeswoman said.

“We think that should be more than sufficient,” the Nixon campaign spokeswoman said.