Hours later, Mr. Cuomo’s camp shot back.

“Lipton joining forces with the pro-Trump, anti-woman and anti-L.G.B.T.Q. Conservative Party proves once and for all that he has no ideology,” said Rich Azzopardi, a senior adviser to Mr. Cuomo. “It’s only about personal power, hypocrisy be damned.”

The W.F.P. lawsuit also shows fault lines in both the Democratic Party in a deep blue state and the all-Democratic Legislature in Albany: the plaintiffs, for example, include a handful of Democratic lawmakers, who have filed a suit against the Assembly speaker, Carl E. Heastie, a Bronx Democrat, and the Senate leader, Andrea Stewart-Cousins, a Democrat from Westchester County.

One of those plaintiffs is Assemblyman Walter T. Mosley, a Democrat from Brooklyn, who said that the fusion voting system was “a valuable part of our election system, which gives voters more choice and brings light to more issues.”

“The creation of a commission aimed at rolling back fusion voting rights was a mistake,” said Mr. Mosley, who said he voted against the budget deal in large part because of the special commission. “And I don’t believe it will hold up in court.”

Many Democrats accept the W.F.P.’s endorsement, but also run on the lines of other parties, too. When the governor was elected to a third term in November, for instance, he ran on four lines, including the Independence Party, a third party which often backs Republicans.

Richard Brodsky, a former state assemblyman and a lawyer for the W.F.P. and other plaintiffs, said that the practice of fusion voting had been a constitutional right for more than a century, and had been repeatedly upheld by the courts.

“We do not have to the prove the wisdom or importance of fusion voting,” said Mr. Brodsky, a Democrat who represented Westchester County. “The other side has to prove why they, by the path of law, should be allowed to interfere with a fundamental constitutional right.”