The Next Battlefield for N.Y. Progressives? The State Assembly.

ALBANY, N.Y. — In the final days of New York’s legislative session, the state’s progressive left-wing seemed poised to score a surprise victory.

A bill that would empower New York to build publicly owned renewable energy was suddenly back in play, after being given up for dead. It cleared the Senate despite sharp opposition from energy producers, and, after hours of fervent grass-roots lobbying, activists proclaimed they had enough votes in the Assembly for passage.

But the Assembly speaker, Carl E. Heastie, never called the bill to the floor, and the session ended with no vote taken.

The inability to force Mr. Heastie’s hand was a glaring example of how the most left-leaning state lawmakers have hit headwinds this year, but it was not the only one: Proposals to protect tenants from evictions, create universal health care, and seal criminal records all fizzled, while landmark progressive changes made in prior years, like the 2019 bail reforms, drew backlash.

The battle over the renewable energy bill served as a reflection of both the growing strength of the party’s left wing and its limitations, especially in the Assembly, which has been controlled by Democrats since 1975.

Now a new slate of left-leaning candidates — some backed by the Working Families Party, others backed by the Democratic Socialists of America — are challenging Democratic incumbents in the June 28 primary, hoping to win enough seats to push the Assembly to the left.

To that end, they’ve aligned their legislative and campaign efforts, urging lawmakers to commit to items like the renewables bill, or face the wrath of progressive voters in primary elections.

Sarahana Shrestha, a climate activist who is running for State Assembly in the Hudson Valley, estimates that her team has knocked on 25,000 doors in the Kingston-based district she hopes to wrest from the Democratic incumbent, Kevin Cahill, who has held the seat since 1992.

She said that the Assembly’s failure to pass the renewable energy bill illustrated how traditional machine politics has led to a broken and undemocratic system.

“That just worked perfectly in our messaging of what’s wrong with our government — the culture of our government,” she said, adding that good governance took courage: “It’s much safer to say, ‘This thing did not happen, this bill did not pass,’ then to pass something and then probably be hounded about it.”

Ms. Shrestha, who is backed by the Democratic Socialists of America and the Working Families Party, has been endorsed by Representative Alexandria Ocasio-Cortez, who has lent the force of her reputation to races up and down New York primary ballots this year, stirring intraparty conflict.

Mr. Cahill, who leads the Assembly Insurance Committee, called it a “power grab.”

“It’s about a group of people in the Assembly and in the Senate who mostly have just arrived on the scene in the last couple of terms who believe that they should be put in charge of the place,” he said. “And they know they can’t do it unless they occupy more seats.”