At its heart, the debate is one between pragmatism and idealism, working within the system versus burning it down.

It is the same debate dogging the Democratic Party at large, but amplified by an only-in-New-York mix of vibrant activism, impenetrably blue politics and — unlike in the rest of the country — still-mighty unions eager to quell perceived threats to their clout.

“Given the political moment we find ourselves in, the idea that a leftist political organization would launch disruptive attacks on their ostensible allies in the labor movement is the definition of cutting off your nose to spite your face,” said Peter Ward, the president of the Hotel Trades Council, a union of hotel workers.

Activists countered that the labor movement had fallen out of step. Jeremy Saunders, the co-executive director of VOCAL-NY, a progressive activism group, said many union leaders seemed dismissive of the energy on the left.

“This growing left sees labor as its natural allies,” he said, “but is frustrated by some unions who too often side with those same politics and politicians who refuse to fight for justice.”

The current dispute involves the New York City branch of the Democratic Socialists of America and the plan it crafted at that basement meeting. The socialists, deeming the city’s unions overly reliant on insider relationships, prepared a “rank-and-file strategy” for their members to join unions and remake them from within.

The group also later published a blog post encouraging other chapters nationwide to follow suit.

Some backlash was immediate. But it exploded recently, after the group’s 37-page memo about its plan was reported by Politico, leading union leaders to accuse D.S.A. of sowing division.